drainagesystem 2026-2-6:20:5:30

AI Linear Algebra/.obsidian/graph.json

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AI Linear Algebra/.obsidian/workspace.json

@@ -13,12 +13,12 @@
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@@ -35,6 +35,86 @@
               "title": "Cardinality"
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@@ -133,7 +213,8 @@
               "title": "Vector Set"
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+    "Cardinality.md",
+    "Basis.md",
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AI Linear Algebra/Magnitude.md

@@ -0,0 +1 @@
+the distance a given vector %%[[Vectors]]%% is from the Null Vector.

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.
+2

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: $||x||+||y|| \geq ||x+y||$

AI Linear Algebra/Normed Spaces.md

@@ -0,0 +1 @@
+[[Vector Spaces]] that have a defined [[Norm]]

AI Linear Algebra/Null Vector.md

@@ -0,0 +1 @@
+an all 0 vector %%[[Vectors]]%%

AI Linear Algebra/P-Norms.md

@@ -0,0 +1,2 @@
+P-norms are a type of [[Norm]] that follows this formula:
+$$‖𝐱‖_𝑝 = \biggl(∑^𝑛_{𝑖=1}|𝑥𝑖|^𝑝\biggr)^{1/𝑝},𝐱 = (𝑥_1, … , 𝑥_𝑛)$$

AI Linear Algebra/Supremum Norm.md

@@ -0,0 +1 @@
+A type of [[Norm]] that is a [[P-Norms]] where the P is ∞