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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
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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
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.
(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
They can also be contained in [[Vector Set]]
(Can also be thought of as a 1 dimensional [[Matrices|Matrix]])