From 61d377de09ff51b59d3d340085aa8dd8298a9414 Mon Sep 17 00:00:00 2001 From: Rivulet Date: Fri, 6 Feb 2026 20:05:30 -0800 Subject: [PATCH] drainagesystem 2026-2-6:20:5:30 --- AI Linear Algebra/.obsidian/graph.json | 2 +- AI Linear Algebra/.obsidian/workspace.json | 107 ++++++++++++++++-- AI Linear Algebra/Magnitude.md | 1 + .../Maximally Linearly Independent.md | 2 +- AI Linear Algebra/Norm.md | 1 + AI Linear Algebra/Normed Spaces.md | 1 + AI Linear Algebra/Null Vector.md | 1 + AI Linear Algebra/P-Norms.md | 2 + AI Linear Algebra/Supremum Norm.md | 1 + 9 files changed, 105 insertions(+), 13 deletions(-) create mode 100644 AI Linear Algebra/Magnitude.md create mode 100644 AI Linear Algebra/Norm.md create mode 100644 AI Linear Algebra/Normed Spaces.md create mode 100644 AI Linear Algebra/Null Vector.md create mode 100644 AI Linear Algebra/P-Norms.md create mode 100644 AI Linear Algebra/Supremum Norm.md diff --git a/AI Linear Algebra/.obsidian/graph.json b/AI Linear Algebra/.obsidian/graph.json index fe2bfe9..ca917b3 100644 --- a/AI Linear Algebra/.obsidian/graph.json +++ b/AI Linear Algebra/.obsidian/graph.json @@ -17,6 +17,6 @@ "repelStrength": 20, "linkStrength": 1, "linkDistance": 30, - "scale": 0.7885418390396122, + "scale": 0.8161147498220488, "close": true } \ No newline at end of file diff --git a/AI Linear Algebra/.obsidian/workspace.json b/AI Linear Algebra/.obsidian/workspace.json index 3054486..61347ee 100644 --- a/AI Linear Algebra/.obsidian/workspace.json +++ b/AI Linear Algebra/.obsidian/workspace.json @@ -13,12 +13,12 @@ "state": { "type": "markdown", "state": { - "file": "Span.md", + "file": "Maximally Linearly Independent.md", "mode": "source", "source": false }, "icon": "lucide-file", - "title": "Span" + "title": "Maximally Linearly Independent" } }, { @@ -35,6 +35,86 @@ "title": "Cardinality" } }, + { + "id": "431933ddf3db8107", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "Magnitude.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "Magnitude" + } + }, + { + "id": "dcbf6d686bbb6536", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "Magnitude.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "Magnitude" + } + }, + { + "id": "815b549b55ef2600", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "Norm.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "Norm" + } + }, + { + "id": "ac134201cd16d907", + "type": "leaf", + "state": { + "type": "graph", + "state": {}, + "icon": "lucide-git-fork", + "title": "Graph view" + } + }, + { + "id": "43e187b2de7fb256", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "P-Norms.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "P-Norms" + } + }, + { + "id": "2c3f77128f00e180", + "type": "leaf", + "state": { + "type": "markdown", + "state": { + "file": "Supremum Norm.md", + "mode": "source", + "source": false + }, + "icon": "lucide-file", + "title": "Supremum Norm" + } + }, { "id": "b3b7ab1942492276", "type": "leaf", @@ -133,7 +213,8 @@ "title": "Vector Set" } } - ] + ], + "currentTab": 7 } ], "direction": "vertical" @@ -206,7 +287,6 @@ "state": { "type": "backlink", "state": { - "file": "Span.md", "collapseAll": false, "extraContext": false, "sortOrder": "alphabetical", @@ -216,7 +296,7 @@ "unlinkedCollapsed": true }, "icon": "links-coming-in", - "title": "Backlinks for Span" + "title": "Backlinks" } }, { @@ -225,12 +305,11 @@ "state": { "type": "outgoing-link", "state": { - "file": "Span.md", "linksCollapsed": false, "unlinkedCollapsed": true }, "icon": "links-going-out", - "title": "Outgoing links from Span" + "title": "Outgoing links" } }, { @@ -296,21 +375,27 @@ "github-sync:Sync with Remote": false } }, - "active": "0c7f6f81494b22b9", + "active": "2c3f77128f00e180", "lastOpenFiles": [ + "P-Norms.md", + "Supremum Norm.md", + "Normed Spaces.md", + "Norm.md", + "Magnitude.md", + "Null Vector.md", + "Cardinality.md", + "Basis.md", + "Span.md", "Vectors.md", "Dimensionality.md", "Vector Set.md", - "Basis.md", "Maximally Linearly Independent.md", "Vector Spaces.md", "Generating Set.md", - "Cardinality.md", "Subspaces.md", "Minimal Generating.md", "Linear Dependency.md", "Linear Combinations.md", - "Span.md", "Non-Trivial.md", "Sets.md", "Welcome.md" diff --git a/AI Linear Algebra/Magnitude.md b/AI Linear Algebra/Magnitude.md new file mode 100644 index 0000000..d4f3bb1 --- /dev/null +++ b/AI Linear Algebra/Magnitude.md @@ -0,0 +1 @@ +the distance a given vector %%[[Vectors]]%% is from the Null Vector. \ No newline at end of file diff --git a/AI Linear Algebra/Maximally Linearly Independent.md b/AI Linear Algebra/Maximally Linearly Independent.md index 2fac00c..d8263ee 100644 --- a/AI Linear Algebra/Maximally Linearly Independent.md +++ b/AI Linear Algebra/Maximally Linearly Independent.md @@ -1 +1 @@ -A form of [[Linear Dependency]] where if even one vector not already present in the [[Vector Set]] is added from the Vector Space %%[[Vector Spaces]]%% it in habits, it is no longer linearly independent. \ No newline at end of file +2 \ No newline at end of file diff --git a/AI Linear Algebra/Norm.md b/AI Linear Algebra/Norm.md new file mode 100644 index 0000000..991268f --- /dev/null +++ b/AI Linear Algebra/Norm.md @@ -0,0 +1 @@ +A norm is a function usually denoted as such: $||x||$ for a vector space %%[[Vector Spaces]]%% that is always greater than zero unless the input value is a [[Null Vector]], has positive homogeneity EX: $|c|*||x|| = ||cx||$, and has Triangle inequality EX: $||x||+||y|| \geq ||x+y||$ \ No newline at end of file diff --git a/AI Linear Algebra/Normed Spaces.md b/AI Linear Algebra/Normed Spaces.md new file mode 100644 index 0000000..2189f6f --- /dev/null +++ b/AI Linear Algebra/Normed Spaces.md @@ -0,0 +1 @@ +[[Vector Spaces]] that have a defined [[Norm]] \ No newline at end of file diff --git a/AI Linear Algebra/Null Vector.md b/AI Linear Algebra/Null Vector.md new file mode 100644 index 0000000..3b56ec9 --- /dev/null +++ b/AI Linear Algebra/Null Vector.md @@ -0,0 +1 @@ +an all 0 vector %%[[Vectors]]%% \ No newline at end of file diff --git a/AI Linear Algebra/P-Norms.md b/AI Linear Algebra/P-Norms.md new file mode 100644 index 0000000..ca1f550 --- /dev/null +++ b/AI Linear Algebra/P-Norms.md @@ -0,0 +1,2 @@ +P-norms are a type of [[Norm]] that follows this formula: +$$‖𝐱‖_𝑝 = \biggl(∑^𝑛_{𝑖=1}|𝑥𝑖|^𝑝\biggr)^{1/𝑝},𝐱 = (𝑥_1, … , 𝑥_𝑛)$$ \ No newline at end of file diff --git a/AI Linear Algebra/Supremum Norm.md b/AI Linear Algebra/Supremum Norm.md new file mode 100644 index 0000000..0d1a5b9 --- /dev/null +++ b/AI Linear Algebra/Supremum Norm.md @@ -0,0 +1 @@ +A type of [[Norm]] that is a [[P-Norms]] where the P is ∞ \ No newline at end of file