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drainagesystem 2026-4-20:19:7:15

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2026-04-20 19:07:15 -07:00
parent 7bb5d5d762
commit ada462624e
17 changed files with 178 additions and 37 deletions
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6
AI Linear Algebra/.obsidian/graph.json vendored
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AI Linear Algebra/Bi-linearity.md Normal file
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A property of 2D functions that says both axes are linear no matter what.
%%related to [[Vectors]]%%

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AI Linear Algebra/Bijective Transformations.md Normal file
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Bijective transformations are both [[Surjective Transformations|Surjective]] and [[Injective Transformations|Injective]].

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AI Linear Algebra/Cosine Similarity.md Normal file
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The cosine similarity is a way to measure the similarity of [[Vectors]]. It is defined as: $$cos(𝐱,𝐲)=\Biggl \langle\frac{𝐱}{‖𝐱‖},\frac{𝐲}{‖𝐲‖} \Biggr \rangle$$

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AI Linear Algebra/Gram-Schmidt orthogonalization process.md Normal file
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A process that takes a [[Linear Dependency|Linearly Independent]] [[Basis]] and creates an [[Orthogonality|Orthogonal]] [[Basis]] that produces the same [[Vector Spaces|Vector Space]] as the original [[Basis]].

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AI Linear Algebra/Injective Transformations.md Normal file
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Injective [[Transformation|Transformations]] are a type of transformation that distinctly maps between [[Vector Spaces]].

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AI Linear Algebra/Inner Product Spaces.md Normal file
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Inner Product Spaces are [[Vector Spaces]] that have an [[Inner Products|Inner Product]]

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AI Linear Algebra/Inner Products.md
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The inner product is a operation that takes in two [[Vectors]] and outputs a number The inner product is a operation that takes in two [[Vectors]] and outputs a number
where the inner product can be defined like this: $⟨𝐱, 𝐲⟩ =∑^𝑛_{𝑖=1}𝑥_𝑖𝑦_𝑖$ where the inner product can be defined like this: $⟨𝐱, 𝐲⟩ =∑^𝑛_{𝑖=1}𝑥_𝑖𝑦_𝑖$
inner products have the unique property that if two vectors are orthogonal from each other that their inner product is 0. inner products have the unique property that if two vectors are orthogonal from each other that their inner product is 0.
(This process is also know as a dot product)

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AI Linear Algebra/Linear Transformation.md Normal file
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A [[Transformation]] is linear if the transformation can be expressed like this: $𝑓(𝑎𝐱 + 𝑏𝐲) = 𝑎𝑓 (𝐱) + 𝑏𝑓 (𝐲)$

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AI Linear Algebra/Matrices.md Normal file
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Matrices are a multidimensional array of numbers that can be operated on.

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AI Linear Algebra/Matrix Multiplication.md Normal file
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Matrix multiplication is an operation on two [[Matrices]] where each row of the first matrix is scaled and summed up by the second.
![[Pasted image 20260420174553.png]]

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AI Linear Algebra/Orthogonality.md Normal file
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A property of a [[Basis]] that says all elements are orthogonal.

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AI Linear Algebra/Surjective Transformations.md Normal file
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Surjective [[Transformation|Transformations]] are transformations that map one [[Vector Spaces|Vector Space]] onto another but are lossy and can include repeats.

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AI Linear Algebra/Transformation.md Normal file
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An operation on [[Vectors]] or [[Matrices]]

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AI Linear Algebra/Vectors.md
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Vectors are a finite list of values Vectors are a finite list of values
They can also be contained in [[Vector Set]] They can also be contained in [[Vector Set]]
(Can also be thought of as a 1 dimensional [[Matrices|Matrix]])