vault backup: 2026-03-05 16:54:10

.obsidian/appearance.json

@@ -1,4 +1,5 @@
 {
   "cssTheme": "Catppuccin",
-  "baseFontSize": 20
+  "baseFontSize": 20,
+  "nativeMenus": true
 }

.obsidian/community-plugins.json

@@ -1,6 +1,7 @@
 [
   "obsidian-git",
   "obsidian-style-settings",
+  "obsidian-completr",
   "obsidian-tikzjax",
-  "obsidian-completr"
+  "obsidian-desmos"
 ]

.obsidian/plugins/obsidian-completr/scanned_words.txt

@@ -41,6 +41,7 @@ EdNL
 Ez
 Exemple
 Element
+Endast
 linjärt
 ller
 linjär
@@ -75,6 +76,10 @@ lyfter
 linjära
 lösningarna
 lönsing
+längd
+läst
+leka
+liksidiga
 ekvationssystem
 en
 ekvationer
@@ -118,6 +123,11 @@ endast
 egenvektorer
 exakt
 entydig
+entydligt
+enhetsmatrisen
+enher
+enhet
+enheter
 med
 moam
 matris
@@ -155,6 +165,7 @@ multiplicitet
 mot
 möjliga
 matriserns
+medger
 reella
 rella
 rektagulär
@@ -239,6 +250,10 @@ kolunrummet
 kärna
 kärnrum
 kolomn
+korninatsystemet
+kombination
+korndinaterna
+kordinater
 är
 än
 ändpunkten
@@ -302,6 +317,14 @@ sammanfaller
 shcema
 schemat
 shcemat
+ska
+ste
+skrivas
+standerndbasen
+standerdbasen
+signerade
+sägs
+späns
 av
 alla
 allmänt
@@ -341,6 +364,8 @@ alltid
 antaliet
 antingen
 aldrig
+area
+arean
 där
 det
 den
@@ -420,6 +445,8 @@ index
 ich
 ibland
 ingen
+inversom
+istället
 variabler
 vatiabler
 vatiable
@@ -448,6 +475,14 @@ vanliga
 vet
 vata
 vektorer
+varja
+vektoter
+vekrje
+vidare
+vektorerna
+varandra
+vektoerna
+viktigt
 och
 om
 ordning
@@ -476,6 +511,16 @@ ojämt
 ohc
 oberoende
 overrightarrow
+ortagonal
+olika
+ortekonala
+ortogonal
+ortogonala
+ortognala
+ortiginal
+oss
+ordingen
+orienterad
 hat
 herstamade
 här
@@ -513,6 +558,7 @@ gG
 general
 genom
 gra
+gälla
 för
 förekommer
 första
@@ -547,6 +593,7 @@ find
 finnas
 fortsätning
 fira
+fallet
 term
 tal
 till
@@ -588,6 +635,10 @@ tänkas
 tvp
 tredhe
 ty
+tt
+tirangel
+tar
+triageln
 ut
 utgöt
 under
@@ -605,6 +656,10 @@ uppfyller
 utvald
 upprepas
 uppn
+up
+utgörs
+underförst
+uo
 HL
 Hur
 HmE
@@ -635,6 +690,7 @@ Similarly
 Som
 SATS
 Samma
+Standerdbasen
 börjar
 bestämmer
 befiner
@@ -661,6 +717,8 @@ beroende
 byten
 bort
 bestämnda
+bas
+beräknar
 Ur
 Under
 Uk
@@ -691,6 +749,11 @@ parytor
 polynom
 produkten
 prisis
+parallellogramet
+pratar
+parallellogramen
+positiv
+parallella
 Alla
 Antigen
 Avslutande
@@ -704,6 +767,8 @@ At
 Aa
 AT
 Användiongs
+Anars
+Areabyte
 Oändligt
 Om
 OBS
@@ -788,6 +853,7 @@ Then
 Transponering
 Transponanten
 Transponaten
+Tv
 Falsk
 För
 Funktionen
@@ -816,6 +882,8 @@ Koraste
 KZ
 Koordinatrummet
 Kallas
+Kom
+Kolumnerna
 Primärfunktioner
 Produkt
 Paramaterformen
@@ -847,11 +915,13 @@ It
 In
 Inverse
 Imdermatrosem
+Ih
 Bestäm
 Betäkning
 Bmm
 BD
 BEVIS
+Betrakta
 öppet
 över
 cos
@@ -913,6 +983,7 @@ jmm
 jS
 jjj
 jämnt
+jobbar
 XmE
 XG
 Xg

.obsidian/plugins/obsidian-desmos/data.json

@@ -0,0 +1,8 @@
+{
+  "version": "0.6.8",
+  "renderer": true,
+  "cache": {
+    "enabled": true,
+    "location": "Memory"
+  }
+}

.obsidian/plugins/obsidian-desmos/manifest.json

@@ -0,0 +1,8 @@
+{
+    "id": "obsidian-desmos",
+    "name": "Desmos",
+    "version": "0.6.8",
+    "minAppVersion": "0.9.12",
+    "description": "Embed Desmos graphs into your notes",
+    "author": "Nigecat"
+}

.obsidian/plugins/obsidian-git/manifest.json

@@ -6,5 +6,5 @@
     "description": "Integrate Git version control with automatic backup and other advanced features.",
     "isDesktopOnly": false,
     "fundingUrl": "https://ko-fi.com/vinzent",
-    "version": "2.35.1"
+    "version": "2.38.0"
 }

.obsidian/plugins/obsidian-git/styles.css

@@ -8,6 +8,15 @@
     }
 }
 
+.git-signs-gutter {
+    .cm-gutterElement {
+        /* Needed to align the sign properly for different line heigts. Such as
+         * when having a heading or list item.
+         */
+        padding-top: 0 !important;
+    }
+}
+
 .workspace-leaf-content[data-type="git-view"] .button-border {
     border: 2px solid var(--interactive-accent);
     border-radius: var(--radius-s);
@@ -72,6 +81,11 @@
     height: 100%;
 }
 
+/* Re-enable wrapping of nav buttns to prevent overflow on smaller screens #*/
+.workspace-drawer .git-view .nav-buttons-container {
+    flex-wrap: wrap;
+}
+
 .git-tools {
     display: flex;
     margin-left: auto;
@@ -129,54 +143,96 @@
     color: var(--text-accent);
 }
 
-.workspace-leaf-content[data-type="diff-view"] .d2h-d-none {
+/* ====== diff2html ======
+The following styles are adapted from the obsidian-version-history plugin by
+@kometenstaub https://github.com/kometenstaub/obsidian-version-history-diff/blob/main/src/styles.scss
+which itself is adapted from the diff2html library with the following original license:
+
+   	https://github.com/rtfpessoa/diff2html/blob/master/LICENSE.md
+
+	Copyright 2014-2016 Rodrigo Fernandes https://rtfpessoa.github.io/
+
+	Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
+	documentation files (the "Software"), to deal in the Software without restriction, including without limitation the
+	rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit
+	persons to whom the Software is furnished to do so, subject to the following conditions:
+
+	The above copyright notice and this permission notice shall be included in all copies or substantial portions of the
+	Software.
+
+	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
+	WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
+	COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+	OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+*/
+
+.theme-dark,
+.theme-light {
+    --git-delete-bg: #ff475040;
+    --git-delete-hl: #96050a75;
+    --git-insert-bg: #68d36840;
+    --git-insert-hl: #23c02350;
+    --git-change-bg: #ffd55840;
+    --git-selected: #3572b0;
+
+    --git-delete: #c33;
+    --git-insert: #399839;
+    --git-change: #d0b44c;
+    --git-move: #3572b0;
+}
+
+.git-diff {
+    .d2h-d-none {
         display: none;
-}
+    }
-
+    .d2h-wrapper {
-.workspace-leaf-content[data-type="diff-view"] .d2h-wrapper {
         text-align: left;
-}
+        border-radius: 0.25em;
-
+        overflow: auto;
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-header {
+    }
-    background-color: var(--background-primary);
+    .d2h-file-header.d2h-file-header {
-    border-bottom: 1px solid var(--interactive-accent);
+        background-color: var(--background-secondary);
-    font-family: var(--font-monospace);
+        border-bottom: 1px solid var(--background-modifier-border);
+        font-family:
+            Source Sans Pro,
+            Helvetica Neue,
+            Helvetica,
+            Arial,
+            sans-serif;
         height: 35px;
         padding: 5px 10px;
-}
+    }
-
+    .d2h-file-header,
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-header,
+    .d2h-file-stats {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-stats {
         display: -webkit-box;
         display: -ms-flexbox;
         display: flex;
-}
+    }
-
+    .d2h-file-header {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-stats {
+        display: none;
+    }
+    .d2h-file-stats {
         font-size: 14px;
         margin-left: auto;
-}
+    }
-
+    .d2h-lines-added {
-.workspace-leaf-content[data-type="diff-view"] .d2h-lines-added {
+        border: 1px solid var(--color-green);
-    border: 1px solid #b4e2b4;
         border-radius: 5px 0 0 5px;
-    color: #399839;
+        color: var(--color-green);
         padding: 2px;
         text-align: right;
         vertical-align: middle;
-}
+    }
-
+    .d2h-lines-deleted {
-.workspace-leaf-content[data-type="diff-view"] .d2h-lines-deleted {
+        border: 1px solid var(--color-red);
-    border: 1px solid #e9aeae;
         border-radius: 0 5px 5px 0;
-    color: #c33;
+        color: var(--color-red);
         margin-left: 1px;
         padding: 2px;
         text-align: left;
         vertical-align: middle;
-}
+    }
-
+    .d2h-file-name-wrapper {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-name-wrapper {
         -webkit-box-align: center;
         -ms-flex-align: center;
         align-items: center;
@@ -185,73 +241,71 @@
         display: flex;
         font-size: 15px;
         width: 100%;
-}
+    }
-
+    .d2h-file-name {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-name {
+        overflow: hidden;
-    overflow-x: hidden;
         text-overflow: ellipsis;
         white-space: nowrap;
-}
+        color: var(--text-normal);
-
+        font-size: var(--h5-size);
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-wrapper {
+    }
-    border: 1px solid var(--background-modifier-border);
+    .d2h-file-wrapper {
+        border: 1px solid var(--background-secondary-alt);
         border-radius: 3px;
         margin-bottom: 1em;
-}
+        max-height: 100%;
-
+    }
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-collapse {
+    .d2h-file-collapse {
         -webkit-box-pack: end;
         -ms-flex-pack: end;
         -webkit-box-align: center;
         -ms-flex-align: center;
         align-items: center;
-    border: 1px solid var(--background-modifier-border);
+        border: 1px solid var(--background-secondary-alt);
         border-radius: 3px;
         cursor: pointer;
         display: none;
         font-size: 12px;
         justify-content: flex-end;
         padding: 4px 8px;
-}
+    }
-
+    .d2h-file-collapse.d2h-selected {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-collapse.d2h-selected {
+        background-color: var(--git-selected);
-    background-color: #c8e1ff;
+    }
-}
+    .d2h-file-collapse-input {
-
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-collapse-input {
         margin: 0 4px 0 0;
-}
+    }
-
+    .d2h-diff-table {
-.workspace-leaf-content[data-type="diff-view"] .d2h-diff-table {
         border-collapse: collapse;
-    font-family: Menlo, Consolas, monospace;
+        font-family: var(--font-monospace);
-    font-size: 13px;
+        font-size: var(--code-size);
         width: 100%;
-}
+    }
-
+    .d2h-files-diff {
-.workspace-leaf-content[data-type="diff-view"] .d2h-files-diff {
         width: 100%;
-}
+    }
-
+    .d2h-file-diff {
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-diff {
+        /*
-    overflow-y: hidden;
+		overflow-y: scroll;
-}
+		*/
-
+        border-radius: 5px;
-.workspace-leaf-content[data-type="diff-view"] .d2h-file-side-diff {
+        font-size: var(--font-text-size);
+        line-height: var(--line-height-normal);
+    }
+    .d2h-file-side-diff {
         display: inline-block;
         margin-bottom: -8px;
         margin-right: -4px;
         overflow-x: scroll;
         overflow-y: hidden;
         width: 50%;
-}
+    }
-
+    .d2h-code-line {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line {
+        padding-left: 6em;
-    padding: 0 8em;
+        padding-right: 1.5em;
-}
+    }
-
+    .d2h-code-line,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line,
+    .d2h-code-side-line {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line {
         display: inline-block;
         -webkit-user-select: none;
         -moz-user-select: none;
@@ -259,13 +313,13 @@
         user-select: none;
         white-space: nowrap;
         width: 100%;
-}
+    }
-
+    .d2h-code-side-line {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line {
+        /* needed to be changed */
-    padding: 0 4.5em;
+        padding-left: 0.5em;
-}
+        padding-right: 0.5em;
-
+    }
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line-ctn {
+    .d2h-code-line-ctn {
         word-wrap: normal;
         background: none;
         display: inline-block;
@@ -275,298 +329,215 @@
         -ms-user-select: text;
         user-select: text;
         vertical-align: middle;
-    white-space: pre;
         width: 100%;
-}
+        /* only works for line-by-line */
-
+        white-space: pre-wrap;
-.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-code-line del,
+    }
-.theme-light
+    .d2h-code-line del,
-    .workspace-leaf-content[data-type="diff-view"]
+    .d2h-code-side-line del {
-    .d2h-code-side-line
+        background-color: var(--git-delete-hl);
-    del {
+        color: var(--text-normal);
-    background-color: #ffb6ba;
+    }
-}
+    .d2h-code-line del,
-
+    .d2h-code-line ins,
-.theme-dark .workspace-leaf-content[data-type="diff-view"] .d2h-code-line del,
+    .d2h-code-side-line del,
-.theme-dark
+    .d2h-code-side-line ins {
-    .workspace-leaf-content[data-type="diff-view"]
-    .d2h-code-side-line
-    del {
-    background-color: #8d232881;
-}
-
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line del,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line ins,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line del,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line ins {
         border-radius: 0.2em;
         display: inline-block;
         margin-top: -1px;
         text-decoration: none;
         vertical-align: middle;
-}
+    }
-
+    .d2h-code-line ins,
-.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-code-line ins,
+    .d2h-code-side-line ins {
-.theme-light
+        background-color: var(--git-insert-hl);
-    .workspace-leaf-content[data-type="diff-view"]
-    .d2h-code-side-line
-    ins {
-    background-color: #97f295;
         text-align: left;
-}
+    }
-
+    .d2h-code-line-prefix {
-.theme-dark .workspace-leaf-content[data-type="diff-view"] .d2h-code-line ins,
-.theme-dark
-    .workspace-leaf-content[data-type="diff-view"]
-    .d2h-code-side-line
-    ins {
-    background-color: #1d921996;
-    text-align: left;
-}
-
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line-prefix {
         word-wrap: normal;
         background: none;
         display: inline;
         padding: 0;
         white-space: pre;
-}
+    }
-
+    .line-num1 {
-.workspace-leaf-content[data-type="diff-view"] .line-num1 {
         float: left;
-}
+    }
-
+    .line-num1,
-.workspace-leaf-content[data-type="diff-view"] .line-num1,
+    .line-num2 {
-.workspace-leaf-content[data-type="diff-view"] .line-num2 {
         -webkit-box-sizing: border-box;
         box-sizing: border-box;
         overflow: hidden;
+        /*
 		padding: 0 0.5em;
+		*/
         text-overflow: ellipsis;
-    width: 3.5em;
+        width: 2.5em;
-}
+        padding-left: 0;
-
+    }
-.workspace-leaf-content[data-type="diff-view"] .line-num2 {
+    .line-num2 {
         float: right;
-}
+    }
-
+    .d2h-code-linenumber {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber {
         background-color: var(--background-primary);
         border: solid var(--background-modifier-border);
         border-width: 0 1px;
         -webkit-box-sizing: border-box;
         box-sizing: border-box;
-    color: var(--text-muted);
+        color: var(--text-faint);
         cursor: pointer;
         display: inline-block;
         position: absolute;
         text-align: right;
-    width: 7.5em;
+        width: 5.5em;
-}
+    }
-
+    .d2h-code-linenumber:after {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber:after {
         content: "\200b";
-}
+    }
-
+    .d2h-code-side-linenumber {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber {
         background-color: var(--background-primary);
         border: solid var(--background-modifier-border);
         border-width: 0 1px;
         -webkit-box-sizing: border-box;
         box-sizing: border-box;
-    color: var(--text-muted);
+        color: var(--text-faint);
         cursor: pointer;
-    display: inline-block;
         overflow: hidden;
         padding: 0 0.5em;
-    position: absolute;
         text-align: right;
         text-overflow: ellipsis;
         width: 4em;
-}
+        /* needed to be changed */
-
+        display: table-cell;
-.workspace-leaf-content[data-type="diff-view"] .d2h-diff-tbody tr {
         position: relative;
-}
+    }
-
+    .d2h-code-side-linenumber:after {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber:after {
         content: "\200b";
-}
+    }
-
+    .d2h-code-side-emptyplaceholder,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-emptyplaceholder,
+    .d2h-emptyplaceholder {
-.workspace-leaf-content[data-type="diff-view"] .d2h-emptyplaceholder {
         background-color: var(--background-primary);
         border-color: var(--background-modifier-border);
-}
+    }
-
+    .d2h-code-line-prefix,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-line-prefix,
+    .d2h-code-linenumber,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber,
+    .d2h-code-side-linenumber,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber,
+    .d2h-emptyplaceholder {
-.workspace-leaf-content[data-type="diff-view"] .d2h-emptyplaceholder {
         -webkit-user-select: none;
         -moz-user-select: none;
         -ms-user-select: none;
         user-select: none;
-}
+    }
-
+    .d2h-code-linenumber,
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber,
+    .d2h-code-side-linenumber {
-.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber {
         direction: rtl;
-}
+    }
-
+    .d2h-del {
-.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-del {
+        background-color: var(--git-delete-bg);
-    background-color: #fee8e9;
+        border-color: var(--git-delete-hl);
-    border-color: #e9aeae;
+    }
-}
+    .d2h-ins {
-
+        background-color: var(--git-insert-bg);
-.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-ins {
+        border-color: var(--git-insert-hl);
-    background-color: #dfd;
+    }
-    border-color: #b4e2b4;
+    .d2h-info {
-}
-
-.theme-dark .workspace-leaf-content[data-type="diff-view"] .d2h-del {
-    background-color: #521b1d83;
-    border-color: #691d1d73;
-}
-
-.theme-dark .workspace-leaf-content[data-type="diff-view"] .d2h-ins {
-    background-color: rgba(30, 71, 30, 0.5);
-    border-color: #13501381;
-}
-
-.workspace-leaf-content[data-type="diff-view"] .d2h-info {
         background-color: var(--background-primary);
         border-color: var(--background-modifier-border);
+        color: var(--text-faint);
+    }
+    .d2h-del,
+    .d2h-ins,
+    .d2h-file-diff .d2h-change {
         color: var(--text-normal);
-}
+    }
-
+    .d2h-file-diff .d2h-del.d2h-change {
-.theme-light
+        background-color: var(--git-change-bg);
-    .workspace-leaf-content[data-type="diff-view"]
+    }
-    .d2h-file-diff
+    .d2h-file-diff .d2h-ins.d2h-change {
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         display: -ms-flexbox;
         display: flex;
         text-align: left;
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+    }
-
+    .d2h-file-list {
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+    }
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+    .d2h-file-list > li {
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         border-bottom: 1px solid var(--background-modifier-border);
         margin: 0;
         padding: 5px 10px;
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+    }
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+    .d2h-file-list > li:last-child {
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+    .d2h-deleted {
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+        color: var(--git-delete);
-    color: #c33;
+    }
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+    .d2h-added {
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+        color: var(--git-insert);
-.workspace-leaf-content[data-type="diff-view"] .d2h-added {
+    }
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+    .d2h-changed {
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+    }
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+    .d2h-tag {
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+        background-color: var(--background-secondary);
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         display: -webkit-box;
         display: -ms-flexbox;
         display: flex;
         font-size: 10px;
         margin-left: 5px;
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+    .d2h-deleted-tag {
+        border: 1px solid var(--git-delete);
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+    .d2h-added-tag {
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+        border: 1px solid var(--git-change);
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-.workspace-leaf-content[data-type="diff-view"] .d2h-deleted-tag {
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 /* ====================== Line Authoring Information ====================== */
@@ -627,3 +598,113 @@
     background: var(--interactive-hover);
     color: var(--text-accent-hover);
 }
+
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+    .cm-gutterElement {
+        display: grid;
+    }
+}
+
+.git-gutter-marker:hover {
+    border-radius: 2px;
+}
+
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+    background-color: var(--color-green);
+    justify-self: center;
+    height: inherit;
+    width: 0.2rem;
+}
+
+.git-gutter-marker.git-change {
+    background-color: var(--color-yellow);
+    justify-self: center;
+    height: inherit;
+    width: 0.2rem;
+}
+
+.git-gutter-marker.git-changedelete {
+    color: var(--color-yellow);
+    font-weight: var(--font-bold);
+    font-size: 1rem;
+    justify-self: center;
+    height: inherit;
+}
+
+.git-gutter-marker.git-delete {
+    background-color: var(--color-red);
+    height: 0.2rem;
+    width: 0.8rem;
+    align-self: end;
+}
+
+.git-gutter-marker.git-topdelete {
+    background-color: var(--color-red);
+    height: 0.2rem;
+    width: 0.8rem;
+    align-self: start;
+}
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+div:hover > .git-gutter-marker.git-change {
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+}
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+div:hover > .git-gutter-marker.git-topdelete {
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+}
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+div:hover > .git-gutter-marker.git-changedelete {
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+}
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+}
+
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+    .cm-merge-revert {
+        width: 4em;
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+    /* Ensure that merge revert markers are positioned correctly */
+    .cm-merge-revert > * {
+        position: absolute;
+        background-color: var(--background-secondary);
+        display: flex;
+    }
+}
+
+/* Prevent shifting of the editor when git signs gutter is the only gutter present */
+.cm-gutters.cm-gutters-before:has(> .git-signs-gutter:only-child) {
+    margin-inline-end: 0;
+    .git-signs-gutter {
+        margin-inline-start: -1rem;
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+}
+
+.git-changes-status-bar-colored {
+    .git-add {
+        color: var(--color-green);
+    }
+    .git-change {
+        color: var(--color-yellow);
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+    .git-delete {
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+}
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+}
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+}

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@@ -4,53 +4,24 @@
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+        "id": "668c17ea9b4a6808",
         "type": "tabs",
         "children": [
           {
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+            "id": "eb1bb5014b86fac7",
             "type": "leaf",
             "state": {
               "type": "markdown",
               "state": {
-                "file": "Determinanter (Kap. 6).md",
+                "file": "Area och Basbyte.md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "Determinanter (Kap. 6)"
+              "title": "Area och Basbyte"
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-              "icon": "lucide-file",
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-                "source": false
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-              "icon": "lucide-file",
-              "title": "Matrisgeometri (Kap 5)"
             }
           }
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-        "currentTab": 2
       }
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     "direction": "vertical"
@@ -209,11 +180,12 @@
       "obsidian-git:Open Git source control": false
     }
   },
-  "active": "bda857902ed8a5fc",
+  "active": "701c0f423bffdcd3",
   "lastOpenFiles": [
-    "Determinanter (Kap. 6).md",
-    "Egenvärderna (Kap 10).md",
     "Matrisgeometri (Kap 5).md",
+    "Egenvärderna (Kap 10).md",
+    "Determinanter (Kap. 6).md",
+    "Area och Basbyte.md",
     "Ekvations System.md",
     "Matriser.md",
     "Vektorer.md",

Area och Basbyte.md

@@ -0,0 +1,73 @@
+```desmos-graph
+left=-5; right=5;
+top=5; bottom=-5;
+---
+([0,0],[0,1])
+([0,1],[0,0])
+0 < y < 1 {0 < x < 1}
+```
+
+*En area enher av parallellogramet som spänns up av vektorerna. Standerdbasen $\overrightarrow{e_1},\;\overrightarrow{e_2}$ utgörs av korndinaterna av* $$\begin{bmatrix}
+1&0\\0&1
+\end{bmatrix}$$
+**DEF**: *En "standerd area enhet" är lika med talet $\det{I}=1$. Om det är underförstått att vi jobbar med standerdbasen, då pratar vi endast om "area enheter".*
+
+**DEF**: *Den signerade arean (dvs. arean med signerade + eller -) av parallellogramen som spänns uo av vektoerna* $$\overrightarrow{u}=(u_1,\;u_2),\;\overrightarrow{v}=(v_1,\;v_2)\in\mathbb{R}^2$$*är leka med determinanten av matrisen vars kolumner utgörs av $\overrightarrow{u}$ och $\overrightarrow{v}$*
+
+*Om vi har en tirangel istället, få tar vi $\frac12$ av den här determinanten*
+**OBS**: *ordingen av $\overrightarrow{u}$ och $\overrightarrow{v}$ är viktigt:*$$\underset{\substack{\parallel\\u_1v_2-v_1u_2}}{\det(\begin{bmatrix}
+u_1&v_1\\u_2&v_2
+\end{bmatrix}}=-1\underset{\substack{\parallel\\v_1u_2-u_1v_2}}{\det(\begin{bmatrix}
+v_1&u_1\\v_2&u_2
+\end{bmatrix}}$$
+
+**DEF** *Två vektorer $\overrightarrow{u},\;\overrightarrow{v}$ sägs vara positiv orienterad om den signerade arean som späns upp av $\overrightarrow{u}$ och $\overrightarrow{v}$ är positiv*
+
+**OBS** *Om $\overrightarrow{u}$ och $\overrightarrow{v}$ är parallella, då*$$\det(\underset{\substack{
+\wedge\\\parallel\\\vee\\
+\text{parallellogramen som spänns up av $\overrightarrow{u}$ och $\overrightarrow{v}$ har area }0
+}}{\begin{bmatrix}
+u_1&v_1\\
+u_2&v_2
+\end{bmatrix}})=0\Leftrightarrow\text{}\text{kolumnerna är linjärt levande}$$
+```desmos-graph
+left=-1; right=5;
+top=1; bottom=-1;
+---
+(1,0.1)|blue|hidden|label:`\overrightarrow{v}`
+(3,0.1)|green|hidden|label:`\overrightarrow{u}`
+([0,2],[0,0])|blue
+([0,4],[0,0])|green
+```
+[Graph of a triangle area]
+*Area av den liksidiga triageln*$$\frac12\det(A)\frac12\times\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}$$
+**Areabyte**:
+- **Kordinater**: $$I\times\begin{bmatrix}
+\zeta_1\\\zeta_2\\\zeta_3
+\end{bmatrix}=A\times\begin{bmatrix}
+\alpha_1\\\alpha_2\\\alpha_3
+\end{bmatrix}$$
+- **Area**: *Om vi hade en area av $X$ a.e. innan basbyte, då har vi $\det{A}\times{X}$ a.e. efter basbyte.*
+- **Volym**: *x v.e. före basbyte $\Rightarrow$ $\det(A)\times{X}$ a.e. efter basbyte.*
+**OBS**:
+- *Area av triangle $=\frac12$ area av parallellogram*
+- *Volum av tetraheder $=\frac13$ volum av parallellepiod*
+- *4-d volum av 4-d tetrahden $=\frac1{24}$ 4-d volum av 4-d parallelopipod*
+
+
+**SATS**: *Låt $A$ vara en $m\times{n}$ ortogonal matris. Då är $\operatorname{def}(A)$ antigen $+1$ eller $-1$.*
+**BEVIS**:
+- *För ortogonala matriser är $A^{-1}=A^T$*
+- *$\det(A)=\det(A^T)$*
+- *$\operatorname{def}(AB)=\operatorname{def}(A)\times\operatorname{def}(B)$*
+$\Rightarrow{A}\times{A^T}=I\Rightarrow\det(AA^T)=\det(I)\Rightarrow\det(A)\times\det{A^T}=1\Rightarrow\operatorname{def}(A)^2=1\Rightarrow\operatorname{def}(A)\text{är }+1\text{ eller }-1$
+**OBS**: *Om vi har en $m\times{n}$ matris $A$, då är $\det(A)$ lika med den $m-$dimensonella volymen av figuren som spenns up av matrises kolumner*
+**EX**: $$\begin{bmatrix}
+1&0\\0&1
+\end{bmatrix}\rightarrow\begin{bmatrix}
+1&\frac12\\
+0&\frac{\sqrt{3}}2
+\end{bmatrix}\Rightarrow\text{svårt att beskriva}$$
+[ ]
+
+**FAKTA**: *Om $A$ är en ortogonal matris, då är skälärprodukten nellan två vektorer samma i så val den gamla basen som den nya basen*