Anki Deck Changes

Commit: 65c49074 - fixed some cards

Author: tprazak <t.prazak@gmail.com>

Date: 2025-12-13T15:16:28+01:00

Changes: 3 note(s) changed (0 added, 3 modified, 0 deleted)

Note 1: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Classic
GUID: s@:duB;6%y
modified

Before

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::1._Definition_and_examples
What special conditions make a set of vectors linearly dependent?

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::1._Definition_and_examples
What special conditions make a set of vectors linearly dependent?
If:
  • one of the vectors is 0
  • one vector \(\textbf{v}\) is contained twice

After

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::1._Definition_and_examples
What special conditions (other than the 3 basic conditions) make a set of vectors linearly dependent?

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::1._Definition_and_examples
What special conditions (other than the 3 basic conditions) make a set of vectors linearly dependent?
If:
  • one of the vectors is 0
  • one vector \(\textbf{v}\) is contained twice
Field-by-field Comparison
Field Before After
Front What special conditions make a set of vectors linearly dependent? What special conditions (other than the 3 basic conditions) make a set of vectors linearly dependent?
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::1._Definition_and_examples

Note 2: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Classic
GUID: m)DHqZ}2Ss
modified

Before

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions of linear dependence:

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions of linear dependence:
  • at least one of the vectors is a linear combination of the other ones
  • there are scalars besides 0, 0, ..., 0 such that \(Ax = 0\). \(\mathbf{0}\) is a nontrivial combination of the vectors.
  • At least one of the vectors is a linear combination of the previous ones

After

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions of linear dependence:

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions of linear dependence:
  • at least one of the vectors is a linear combination of the other ones
  • there are scalars \(\lambda_1, ..., \lambda_n\) besides 0, 0, ..., 0 such that \(\sum_{i = 1}^n \lambda_i v_i = \mathbf{0}\). \(\mathbf{0}\) is a nontrivial combination of the vectors.
  • At least one of the vectors is a linear combination of the previous ones
Field-by-field Comparison
Field Before After
Back <ul><li>at least one of the vectors is a linear combination of the other ones</li><li>there are scalars besides 0, 0, ..., 0 such that&nbsp;\(Ax = 0\).&nbsp;\(\mathbf{0}\)&nbsp;is a nontrivial combination of the vectors.</li><li>At least one of the vectors is a linear combination of the previous ones</li></ul> <ul><li>at least one of the vectors is a linear combination of the other ones</li><li>there are scalars&nbsp;\(\lambda_1, ..., \lambda_n\)&nbsp;besides 0, 0, ..., 0 such that&nbsp;\(\sum_{i = 1}^n \lambda_i v_i = \mathbf{0}\).&nbsp;\(\mathbf{0}\)&nbsp;is a nontrivial combination of the vectors.</li><li>At least one of the vectors is a linear combination of the previous ones</li></ul>
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions

Note 3: ETH::LinAlg

Deck: ETH::LinAlg
Note Type: Horvath Classic
GUID: eY$X2~xJ5/
modified

Before

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions for linear independence

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions for linear independence
  • None of the vectors is a linear combination of the other ones
  • There are no scalars besides 0, 0, ..., 0 such that \(Ax= \mathbf{0}\). \(\mathbf{0}\) can only be written as a trivial combination of the vectors
  • None of the vectors is a linear combination of the previous ones

After

Front

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions for linear independence

Back

ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
Give me the three definitions for linear independence
  • None of the vectors is a linear combination of the other ones
  • There are no scalars  \(\lambda_1, ..., \lambda_n\) besides 0, 0, ..., 0 such that \(\sum_{i = 1}^n \lambda_i v_i = \mathbf{0}\). \(\mathbf{0}\) can only be written as a trivial combination of the vectors
  • None of the vectors is a linear combination of the previous ones
Field-by-field Comparison
Field Before After
Back <ul><li>None of the vectors is a linear combination of the other ones</li><li>There are no scalars besides 0, 0, ..., 0 such that&nbsp;\(Ax= \mathbf{0}\).&nbsp;\(\mathbf{0}\)&nbsp;can only be written as a trivial combination of the vectors</li><li>None of the vectors is a linear combination of the previous ones<br></li></ul> <ul><li>None of the vectors is a linear combination of the other ones</li><li>There are no scalars&nbsp;&nbsp;\(\lambda_1, ..., \lambda_n\)&nbsp;besides 0, 0, ..., 0 such that&nbsp;\(\sum_{i = 1}^n \lambda_i v_i = \mathbf{0}\).&nbsp;\(\mathbf{0}\)&nbsp;can only be written as a trivial combination of the vectors</li><li>None of the vectors is a linear combination of the previous ones<br></li></ul>
Tags: ETH::1._Semester::LinAlg::1._Vectors::3._Linear_(in)dependence::2._Alternative_definitions
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