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my obsidian vault first commit

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Rivulet
2026-01-15 13:56:26 -08:00
commit 1426298b31
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3
AI Linear Algebra/.obsidian/app.json vendored Normal file
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AI Linear Algebra/.obsidian/appearance.json vendored Normal file
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{}

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AI Linear Algebra/.obsidian/community-plugins.json vendored Normal file
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[
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AI Linear Algebra/.obsidian/core-plugins.json vendored Normal file
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AI Linear Algebra/.obsidian/graph.json vendored Normal file
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AI Linear Algebra/.obsidian/plugins/github-sync/main.js vendored Normal file
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AI Linear Algebra/.obsidian/plugins/github-sync/manifest.json vendored Normal file
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AI Linear Algebra/.obsidian/plugins/github-sync/styles.css vendored Normal file
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This CSS file will be included with your plugin, and
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If your plugin does not need CSS, delete this file.
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311
AI Linear Algebra/.obsidian/workspace.json vendored Normal file
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AI Linear Algebra/Basis.md Normal file
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A basis is a [[Generating Set]] that is both [[Maximally Linearly Independent]] and [[Minimal Generating]].
%%[[Vector Set]]%%

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AI Linear Algebra/Cardinality.md Normal file
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the number of [[Vectors]] in a [[Vector Set]]

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AI Linear Algebra/Dimensionality.md Normal file
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the number of values in a vector %%[[Vectors]]%%

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AI Linear Algebra/Generating Set.md Normal file
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A generating set is a [[Vector Set]] that when the [[Span]] function is applied generates another distinct set.

3
AI Linear Algebra/Linear Combinations.md Normal file
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A type of function on a [[Vector Set]] that sums the elements with a corresponding coefficient scalar such as $2x_1+x_2$ or $x_1+x_3$ or for a more generalized equation $\sum_{i=1}^{n}x_i v_i$ where $S = \{v_1,...,v_n\}$ is the vector set and $v_i \in S$ and $x = (x_1,...,x_n)$ is a list of coefficient scalars.
%% Related to [[Vectors]]%%

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AI Linear Algebra/Linear Dependency.md Normal file
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Linear Independence is a classification for a [[Vector Set]] where all [[Vectors]] of the set cannot be made using a [[Non-Trivial]] Linear Combination of the other vectors in the set. Otherwise they are classified as Linearly Dependent

1
AI Linear Algebra/Maximally Linearly Independent.md Normal file
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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.

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AI Linear Algebra/Minimal Generating.md Normal file
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A [[Generating Set]] that will no longer generate the same [[Span]] if even one of its elements is removed
%%[[Vector Set]]%%

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AI Linear Algebra/Non-Trivial.md Normal file
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Any operation not adding a null vector (a completely zeroed out vector) to a vector
An example of these would be Non-Trivial [[Linear Combinations]] which just are combinations which do not involve a null vector

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AI Linear Algebra/Span.md Normal file
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Span is an function that returns a [[Vector Set]] containing all [[Linear Combinations]] for any given vector set.
example: $span(S)$.
also do note that $span(S) = span(span(S))$
you cannot maximize a maximal set.

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AI Linear Algebra/Subspaces.md Normal file
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Subspaces are [[Vector Spaces]] that are a subset of a Vector Space and closed under addition and scalar multiplication.

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AI Linear Algebra/Vector Set.md Normal file
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A set of [[Vectors]] that are unique and of same [[Dimensionality]].

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AI Linear Algebra/Vector Spaces.md Normal file
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A domain of all values that are to be operated in such as the set of all real numbers.
%%Related to [[Vectors]] and [[Vector Set]]s%%

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AI Linear Algebra/Vectors.md Normal file
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Vectors are a finite list of values
They can also be contained in [[Vector Set]]