Anki Deck Changes

Commit: 630493f0 - linalg new cards

Author: obrhubr <obrhubr@gmail.com>

Date: 2025-12-30T10:01:37+01:00

Changes: 10 note(s) changed (6 added, 4 modified, 0 deleted)

ℹ️ Cosmetic Changes Hidden: 1 note(s) had formatting-only changes and are not shown below

Note 1: ETH::EProg

Deck: ETH::EProg
Note Type: Horvath Classic
GUID: Q=BFp=(vY3
modified

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ETH::1._Semester::EProg::3._Control_Structures::1._Branching PlsFix::UNclozeThatBish
The ternary operator has the following syntax:

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ETH::1._Semester::EProg::3._Control_Structures::1._Branching PlsFix::UNclozeThatBish
The ternary operator has the following syntax:

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ETH::1._Semester::EProg::3._Control_Structures::1._Branching
The ternary operator has the following syntax:

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ETH::1._Semester::EProg::3._Control_Structures::1._Branching
The ternary operator has the following syntax:
test ? valueTrue : valueFalse
Field-by-field Comparison
Field Before After
Front The ternary operator has the following syntax: <br><br>{{c1:: test ? valueTrue : valueFalse}} The ternary operator has the following syntax:
Back test ? valueTrue : valueFalse
Tags: PlsFix::UNclozeThatBish ETH::1._Semester::EProg::3._Control_Structures::1._Branching

Note 2: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: col^b$YzMt
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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::2._Euclidean_norm
\(v^\top v = \) \(||v||^2\) (in terms of norm)

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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::2._Euclidean_norm
\(v^\top v = \) \(||v||^2\) (in terms of norm)
as \(||v|| = \sqrt{v^\top v}\).
Field-by-field Comparison
Field Before After
Text \(v^\top v = \){{c1::&nbsp;\(||v||^2\)}} (in terms of norm)
Extra as&nbsp;\(||v|| = \sqrt{v^\top v}\).
Tags: ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::2._Euclidean_norm

Note 3: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Classic
GUID: d4<]X?O^},
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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors
When is \(0 \in \textbf{Span}(\{v_1, \dots, v_n\})\)?

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors
When is \(0 \in \textbf{Span}(\{v_1, \dots, v_n\})\)?
\(0\) is in the span of any vectors, even in the span of the empty set.
Field-by-field Comparison
Field Before After
Front When is&nbsp;\(0 \in \textbf{Span}(\{v_1, \dots, v_n\})\)?
Back \(0\)&nbsp;is in the span of any vectors, even in the span of the empty set.
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors

Note 4: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: gU%jisb2z3
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ETH::1._Semester::LinAlg::1._Vectors::1._Vectors_and_linear_combinations::2._Scalar_multiplication
Scalar product properties: \(u, v, w \in \mathbb{R}^m\) be vectors and \(\lambda \in \mathbb{R}\) a scalar.
  1. \(v \cdot w = w \cdot v\) (symmetry / commutatitivity
  2.  \((\lambda v) \cdot w = \lambda (v \cdot w)\) (scalars move freely)
  3.  \(u \cdot (v + w) = u \cdot v + u \cdot w\) and \((u + v) \cdot w = u\cdot w + v \cdot w\) (distributivity)
  4.  \(v \cdot v \geq 0\) with equality if and only if \(v = 0\) (positive definiteness

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ETH::1._Semester::LinAlg::1._Vectors::1._Vectors_and_linear_combinations::2._Scalar_multiplication
Scalar product properties: \(u, v, w \in \mathbb{R}^m\) be vectors and \(\lambda \in \mathbb{R}\) a scalar.
  1. \(v \cdot w = w \cdot v\) (symmetry / commutatitivity
  2.  \((\lambda v) \cdot w = \lambda (v \cdot w)\) (scalars move freely)
  3.  \(u \cdot (v + w) = u \cdot v + u \cdot w\) and \((u + v) \cdot w = u\cdot w + v \cdot w\) (distributivity)
  4.  \(v \cdot v \geq 0\) with equality if and only if \(v = 0\) (positive definiteness
Field-by-field Comparison
Field Before After
Text Scalar product properties:&nbsp;\(u, v, w \in \mathbb{R}^m\)&nbsp;be vectors and&nbsp;\(\lambda \in \mathbb{R}\)&nbsp;a scalar.<br><ol><li>{{c1::\(v \cdot w = w \cdot v\)&nbsp;(symmetry / commutatitivity}}</li><li>{{c2::&nbsp;\((\lambda v) \cdot w = \lambda (v \cdot w)\)&nbsp;(scalars move freely)}}</li><li>{{c3::&nbsp;\(u \cdot (v + w) = u \cdot v + u \cdot w\)&nbsp;and&nbsp;\((u + v) \cdot w = u\cdot w + v \cdot w\)&nbsp;(distributivity)}}</li><li>{{c4::&nbsp;\(v \cdot v \geq 0\)&nbsp;with equality if and only if&nbsp;\(v = 0\)&nbsp;(positive definiteness}}</li></ol>
Tags: ETH::1._Semester::LinAlg::1._Vectors::1._Vectors_and_linear_combinations::2._Scalar_multiplication

Note 5: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: k_E{8UgRT{
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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::4._Angles
The dimensions of a hyperplane \(H\) through the origin in \(\mathbb{R}^m\) is  \(m - 1\).

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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::4._Angles
The dimensions of a hyperplane \(H\) through the origin in \(\mathbb{R}^m\) is  \(m - 1\).
See assignment 6 proof.
Field-by-field Comparison
Field Before After
Text The dimensions of a hyperplane&nbsp;\(H\)&nbsp;through the origin in&nbsp;\(\mathbb{R}^m\)&nbsp;is {{c1::&nbsp;\(m - 1\)}}.
Extra See assignment 6&nbsp;proof.
Tags: ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::4._Angles

Note 6: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Classic
GUID: ltjw8T1j7K
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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors
The span \(\textbf{Span}(\emptyset)\) is:

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors
The span \(\textbf{Span}(\emptyset)\) is:
\(\{0\}\) only the zero vector, as the empty sum = 0.
Field-by-field Comparison
Field Before After
Front The span&nbsp;\(\textbf{Span}(\emptyset)\)&nbsp;is:
Back \(\{0\}\)&nbsp;only the zero vector, as the empty sum = 0.
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors

Note 7: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: nkL&a6|Q;d
modified

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
The span of m linearly independent vectors is \({{c1::\mathbb{R}^m}}\).

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
The span of m linearly independent vectors is \({{c1::\mathbb{R}^m}}\).
This also means that a matrix in \(\mathbb{R}^{n \times n}\) with rank(A) = n spans the entire space.

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
The span of m linearly independent vectors is {{c1::\(\mathbb{R}^m\)}}.

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
The span of m linearly independent vectors is {{c1::\(\mathbb{R}^m\)}}.
This also means that a matrix in \(\mathbb{R}^{n \times n}\) with rank(A) = n spans the entire space.
Field-by-field Comparison
Field Before After
Text The span of m linearly independent vectors is&nbsp;\({{c1::\mathbb{R}^m}}\). The span of m linearly independent vectors is {{c1::\(\mathbb{R}^m\)}}.
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish

Note 8: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: qGI8y.9F)Z
modified

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
If I add vector v, which is a linear combination of \(v_1, v_2, ..., v_n\) to the span it:

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
If I add vector v, which is a linear combination of \(v_1, v_2, ..., v_n\) to the span it:
does not change

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
If I add vector v, which is a linear combination of \(v_1, v_2, ..., v_n\) to the span it does not change

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ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish
If I add vector v, which is a linear combination of \(v_1, v_2, ..., v_n\) to the span it does not change
Field-by-field Comparison
Field Before After
Text If I add vector v, which is a linear combination of&nbsp;\(v_1, v_2, ..., v_n\)&nbsp;to the span it: If I add vector v, which is a linear combination of&nbsp;\(v_1, v_2, ..., v_n\)&nbsp;to the span it {{c1::does not change}}
Extra does not change
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::3._Span_of_vectors PlsFix::ClozeThatBish

Note 9: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Cloze
GUID: w7_|F6Nt!U
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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::5._Triangle_inequality
The triangle inequality \(||v|| + ||w|| \geq ||v+w||\) holds exactly if \(\exists \lambda \) s.t. \(w = \lambda v\) (i.e. they are scalar multiples)

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ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::5._Triangle_inequality
The triangle inequality \(||v|| + ||w|| \geq ||v+w||\) holds exactly if \(\exists \lambda \) s.t. \(w = \lambda v\) (i.e. they are scalar multiples)
Field-by-field Comparison
Field Before After
Text The triangle inequality&nbsp;\(||v|| + ||w|| \geq ||v+w||\)&nbsp;holds exactly if {{c1::\(\exists \lambda \)&nbsp;s.t.&nbsp;\(w = \lambda v\)&nbsp;(i.e. they are scalar multiples)}}
Tags: ETH::1._Semester::LinAlg::1._Vectors::2._Scalar_products,_lengths_and_angles::5._Triangle_inequality
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