Zacharias/Analys-och-Linj-r-algibra
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

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

Browse Source
This commit is contained in:
Zacharias Zellén
2026-03-05 16:54:10 +01:00
parent 4a5388ed66
commit c2f35479ac
12 changed files with 69896 additions and 743 deletions
Download Patch File Download Diff File Expand all files Collapse all files

3
.obsidian/appearance.json vendored
View File

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

3
.obsidian/community-plugins.json vendored
View File

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

71
.obsidian/plugins/obsidian-completr/scanned_words.txt vendored
View File

@@ -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

8
.obsidian/plugins/obsidian-desmos/data.json vendored Normal file
View File

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

65724
.obsidian/plugins/obsidian-desmos/main.js vendored Normal file
View File

File diff suppressed because one or more lines are too long

8
.obsidian/plugins/obsidian-desmos/manifest.json vendored Normal file
View File

@@ -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"
}

3188
.obsidian/plugins/obsidian-desmos/vendor/desmos.js vendored Normal file
View File

File diff suppressed because one or more lines are too long

556
.obsidian/plugins/obsidian-git/main.js vendored
View File

File diff suppressed because one or more lines are too long

2
.obsidian/plugins/obsidian-git/manifest.json vendored
View File

@@ -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"
}

555
.obsidian/plugins/obsidian-git/styles.css vendored
View File

@@ -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;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-wrapper {
.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);
border-bottom: 1px solid var(--interactive-accent);
font-family: var(--font-monospace);
.d2h-file-header.d2h-file-header {
background-color: var(--background-secondary);
border-bottom: 1px solid var(--background-modifier-border);
font-family:
Source Sans Pro,
Helvetica Neue,
Helvetica,
Arial,
sans-serif;
height: 35px;
padding: 5px 10px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-header,
.workspace-leaf-content[data-type="diff-view"] .d2h-file-stats {
.d2h-file-header,
.d2h-file-stats {
display: -webkit-box;
display: -ms-flexbox;
display: flex;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-stats {
.d2h-file-header {
display: none;
}
.d2h-file-stats {
font-size: 14px;
margin-left: auto;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-lines-added {
border: 1px solid #b4e2b4;
.d2h-lines-added {
border: 1px solid var(--color-green);
border-radius: 5px 0 0 5px;
color: #399839;
color: var(--color-green);
padding: 2px;
text-align: right;
vertical-align: middle;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-lines-deleted {
border: 1px solid #e9aeae;
.d2h-lines-deleted {
border: 1px solid var(--color-red);
border-radius: 0 5px 5px 0;
color: #c33;
color: var(--color-red);
margin-left: 1px;
padding: 2px;
text-align: left;
vertical-align: middle;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-name-wrapper {
.d2h-file-name-wrapper {
-webkit-box-align: center;
-ms-flex-align: center;
align-items: center;
@@ -186,26 +242,26 @@
font-size: 15px;
width: 100%;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-name {
overflow-x: hidden;
.d2h-file-name {
overflow: 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;
@@ -213,31 +269,30 @@
justify-content: flex-end;
padding: 4px 8px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-collapse.d2h-selected {
background-color: #c8e1ff;
.d2h-file-collapse.d2h-selected {
background-color: var(--git-selected);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-collapse-input {
.d2h-file-collapse-input {
margin: 0 4px 0 0;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-diff-table {
.d2h-diff-table {
border-collapse: collapse;
font-family: Menlo, Consolas, monospace;
font-size: 13px;
font-family: var(--font-monospace);
font-size: var(--code-size);
width: 100%;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-files-diff {
.d2h-files-diff {
width: 100%;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-diff {
overflow-y: hidden;
.d2h-file-diff {
/*
overflow-y: scroll;
*/
border-radius: 5px;
font-size: var(--font-text-size);
line-height: var(--line-height-normal);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-side-diff {
.d2h-file-side-diff {
display: inline-block;
margin-bottom: -8px;
margin-right: -4px;
@@ -245,13 +300,12 @@
overflow-y: hidden;
width: 50%;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-line {
padding: 0 8em;
.d2h-code-line {
padding-left: 6em;
padding-right: 1.5em;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-line,
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line {
.d2h-code-line,
.d2h-code-side-line {
display: inline-block;
-webkit-user-select: none;
-moz-user-select: none;
@@ -260,12 +314,12 @@
white-space: nowrap;
width: 100%;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-line {
padding: 0 4.5em;
.d2h-code-side-line {
/* needed to be changed */
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;
@@ -275,276 +329,190 @@
-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
.workspace-leaf-content[data-type="diff-view"]
.d2h-code-side-line
del {
background-color: #ffb6ba;
.d2h-code-line del,
.d2h-code-side-line del {
background-color: var(--git-delete-hl);
color: var(--text-normal);
}
.theme-dark .workspace-leaf-content[data-type="diff-view"] .d2h-code-line del,
.theme-dark
.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 {
.d2h-code-line del,
.d2h-code-line ins,
.d2h-code-side-line del,
.d2h-code-side-line ins {
border-radius: 0.2em;
display: inline-block;
margin-top: -1px;
text-decoration: none;
vertical-align: middle;
}
.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-code-line ins,
.theme-light
.workspace-leaf-content[data-type="diff-view"]
.d2h-code-side-line
ins {
background-color: #97f295;
.d2h-code-line ins,
.d2h-code-side-line ins {
background-color: var(--git-insert-hl);
text-align: left;
}
.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 {
.d2h-code-line-prefix {
word-wrap: normal;
background: none;
display: inline;
padding: 0;
white-space: pre;
}
.workspace-leaf-content[data-type="diff-view"] .line-num1 {
.line-num1 {
float: left;
}
.workspace-leaf-content[data-type="diff-view"] .line-num1,
.workspace-leaf-content[data-type="diff-view"] .line-num2 {
.line-num1,
.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;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber {
.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;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber:after {
.d2h-code-linenumber:after {
content: "\200b";
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber {
.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;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-diff-tbody tr {
/* needed to be changed */
display: table-cell;
position: relative;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber:after {
.d2h-code-side-linenumber:after {
content: "\200b";
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-emptyplaceholder,
.workspace-leaf-content[data-type="diff-view"] .d2h-emptyplaceholder {
.d2h-code-side-emptyplaceholder,
.d2h-emptyplaceholder {
background-color: var(--background-primary);
border-color: var(--background-modifier-border);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-line-prefix,
.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber,
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber,
.workspace-leaf-content[data-type="diff-view"] .d2h-emptyplaceholder {
.d2h-code-line-prefix,
.d2h-code-linenumber,
.d2h-code-side-linenumber,
.d2h-emptyplaceholder {
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-code-linenumber,
.workspace-leaf-content[data-type="diff-view"] .d2h-code-side-linenumber {
.d2h-code-linenumber,
.d2h-code-side-linenumber {
direction: rtl;
}
.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-del {
background-color: #fee8e9;
border-color: #e9aeae;
.d2h-del {
background-color: var(--git-delete-bg);
border-color: var(--git-delete-hl);
}
.theme-light .workspace-leaf-content[data-type="diff-view"] .d2h-ins {
background-color: #dfd;
border-color: #b4e2b4;
.d2h-ins {
background-color: var(--git-insert-bg);
border-color: var(--git-insert-hl);
}
.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 {
.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);
}
.theme-light
.workspace-leaf-content[data-type="diff-view"]
.d2h-file-diff
.d2h-del.d2h-change {
background-color: #fdf2d0;
.d2h-file-diff .d2h-del.d2h-change {
background-color: var(--git-change-bg);
}
.theme-dark
.workspace-leaf-content[data-type="diff-view"]
.d2h-file-diff
.d2h-del.d2h-change {
background-color: #55492480;
.d2h-file-diff .d2h-ins.d2h-change {
background-color: var(--git-insert-bg);
}
.theme-light
.workspace-leaf-content[data-type="diff-view"]
.d2h-file-diff
.d2h-ins.d2h-change {
background-color: #ded;
}
.theme-dark
.workspace-leaf-content[data-type="diff-view"]
.d2h-file-diff
.d2h-ins.d2h-change {
background-color: rgba(37, 78, 37, 0.418);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list-wrapper {
margin-bottom: 10px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list-wrapper a {
color: #3572b0;
.d2h-file-list-wrapper {
a {
text-decoration: none;
cursor: default;
-webkit-user-drag: none;
}
.workspace-leaf-content[data-type="diff-view"]
.d2h-file-list-wrapper
a:visited {
color: #3572b0;
svg {
display: none;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list-header {
}
.d2h-file-list-header {
text-align: left;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list-title {
font-weight: 700;
.d2h-file-list-title {
display: none;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list-line {
.d2h-file-list-line {
display: -webkit-box;
display: -ms-flexbox;
display: flex;
text-align: left;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list {
display: block;
list-style: none;
margin: 0;
padding: 0;
.d2h-file-list {
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list > li {
.d2h-file-list > li {
border-bottom: 1px solid var(--background-modifier-border);
margin: 0;
padding: 5px 10px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-list > li:last-child {
.d2h-file-list > li:last-child {
border-bottom: none;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-file-switch {
.d2h-file-switch {
cursor: pointer;
display: none;
font-size: 10px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-icon {
.d2h-icon {
fill: currentColor;
margin-right: 10px;
vertical-align: middle;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-deleted {
color: #c33;
.d2h-deleted {
color: var(--git-delete);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-added {
color: #399839;
.d2h-added {
color: var(--git-insert);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-changed {
color: #d0b44c;
.d2h-changed {
color: var(--git-change);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-moved {
color: #3572b0;
.d2h-moved {
color: var(--git-move);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-tag {
background-color: var(--background-primary);
.d2h-tag {
background-color: var(--background-secondary);
display: -webkit-box;
display: -ms-flexbox;
display: flex;
@@ -552,21 +520,24 @@
margin-left: 5px;
padding: 0 2px;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-deleted-tag {
border: 2px solid #c33;
.d2h-deleted-tag {
border: 1px solid var(--git-delete);
}
.d2h-added-tag {
border: 1px solid var(--git-insert);
}
.d2h-changed-tag {
border: 1px solid var(--git-change);
}
.d2h-moved-tag {
border: 1px solid var(--git-move);
}
.workspace-leaf-content[data-type="diff-view"] .d2h-added-tag {
border: 1px solid #399839;
}
/* needed for line-by-line*/
.workspace-leaf-content[data-type="diff-view"] .d2h-changed-tag {
border: 1px solid #d0b44c;
.d2h-diff-tbody {
position: relative;
}
.workspace-leaf-content[data-type="diff-view"] .d2h-moved-tag {
border: 1px solid #3572b0;
}
/* ====================== Line Authoring Information ====================== */
@@ -627,3 +598,113 @@
background: var(--interactive-hover);
color: var(--text-accent-hover);
}
.git-signs-gutter {
.cm-gutterElement {
display: grid;
}
}
.git-gutter-marker:hover {
border-radius: 2px;
}
.git-gutter-marker.git-add {
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;
}
div:hover > .git-gutter-marker.git-change {
width: 0.6rem;
}
div:hover > .git-gutter-marker.git-add {
width: 0.6rem;
}
div:hover > .git-gutter-marker.git-delete {
height: 0.6rem;
}
div:hover > .git-gutter-marker.git-topdelete {
height: 0.6rem;
}
div:hover > .git-gutter-marker.git-changedelete {
font-weight: var(--font-bold);
}
.git-gutter-marker.staged {
opacity: 0.5;
}
.git-diff {
.cm-merge-revert {
width: 4em;
}
/* 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;
}
}
.git-changes-status-bar-colored {
.git-add {
color: var(--color-green);
}
.git-change {
color: var(--color-yellow);
}
.git-delete {
color: var(--color-red);
}
}
.git-changes-status-bar .git-add {
margin-right: 0.3em;
}
.git-changes-status-bar .git-change {
margin-right: 0.3em;
}

46
.obsidian/workspace.json vendored
View File

@@ -4,53 +4,24 @@
"type": "split",
"children": [
{
"id": "eec1dd4145fc2eac",
"id": "668c17ea9b4a6808",
"type": "tabs",
"children": [
{
"id": "334286c6c273f693",
"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)"
}
},
{
"id": "80e9057cf6d4aa05",
"type": "leaf",
"state": {
"type": "markdown",
"state": {
"file": "Egenvärderna (Kap 10).md",
"mode": "source",
"source": false
},
"icon": "lucide-file",
"title": "Egenvärderna (Kap 10)"
}
},
{
"id": "bda857902ed8a5fc",
"type": "leaf",
"state": {
"type": "markdown",
"state": {
"file": "Matrisgeometri (Kap 5).md",
"mode": "source",
"source": false
},
"icon": "lucide-file",
"title": "Matrisgeometri (Kap 5)"
"title": "Area och Basbyte"
}
}
],
"currentTab": 2
]
}
],
"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",

73
Area och Basbyte.md Normal file
View File

@@ -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*