User:IssaRice/Linear algebra/Outline of linear algebra - Revision history

IssaRice: IssaRice moved page User:IssaRice/Outline of linear algebra to User:IssaRice/Linear algebra/Outline of linear algebra

2019-01-02T21:28:11Z

← Older revision	Revision as of 21:28, 2 January 2019
(No difference)

2018-12-27T06:15:09Z

First half of linear algebra

← Older revision		Revision as of 06:15, 27 December 2018
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	* Row equivalence (several equivalent formulations)		* Row equivalence (several equivalent formulations)
	* Echelon form, reduced row echelon form, pivots		* Echelon form, reduced row echelon form, pivots
	* Linear independence, span, basis (there seems to be a choice of doing this as sets vs lists)		* Linear independence, span, basis (there seems to be a choice of doing this as sets vs lists, although I think even books that use sets are sometimes forced to then define an "ordered basis")
	* Column space		* Column space
	* Row space		* Row space

2018-12-27T01:34:58Z

First half of linear algebra

← Older revision		Revision as of 01:34, 27 December 2018
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	* Elementary row operations, elementary matrices		* Elementary row operations, elementary matrices
	* Row equivalence		* Row equivalence (several equivalent formulations)
	* Echelon form, reduced row echelon form, pivots		* Echelon form, reduced row echelon form, pivots
	* Linear independence, span, basis (there seems to be a choice of doing this as sets vs lists)		* Linear independence, span, basis (there seems to be a choice of doing this as sets vs lists)

2018-12-27T00:06:29Z

First half of linear algebra

← Older revision		Revision as of 00:06, 27 December 2018
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	* Row equivalence		* Row equivalence
	* Echelon form, reduced row echelon form, pivots		* Echelon form, reduced row echelon form, pivots
	* Linear independence, span, basis		* Linear independence, span, basis (there seems to be a choice of doing this as sets vs lists)
	* Column space		* Column space
	* Row space		* Row space

2018-12-27T00:02:36Z

First half of linear algebra

← Older revision		Revision as of 00:02, 27 December 2018
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	* Fundamental theorem of linear maps: rank + nullity = dimension of domain		* Fundamental theorem of linear maps: rank + nullity = dimension of domain
	* Equivalent properties of injective, surjective, bijective		* Equivalent properties of injective, surjective, bijective
			* Change of basis
			* Matrix similarity
	* Going back and forth between coordinate-based and coordinate-free approach, e.g. diagonalization via multiplying on both sides vs diagonalization via picking some basis		* Going back and forth between coordinate-based and coordinate-free approach, e.g. diagonalization via multiplying on both sides vs diagonalization via picking some basis

2018-12-26T22:55:41Z

First half of linear algebra

← Older revision		Revision as of 22:55, 26 December 2018
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	* Fundamental theorem of linear maps: rank + nullity = dimension of domain		* Fundamental theorem of linear maps: rank + nullity = dimension of domain
	* Equivalent properties of injective, surjective, bijective		* Equivalent properties of injective, surjective, bijective
			* Going back and forth between coordinate-based and coordinate-free approach, e.g. diagonalization via multiplying on both sides vs diagonalization via picking some basis

	==Second half of linear algebra==		==Second half of linear algebra==

2018-12-26T22:51:05Z

← Older revision		Revision as of 22:51, 26 December 2018
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	* Orthonormal bases		* Orthonormal bases
	* Orthogonal projection		* Orthogonal projection

			==Questions==

			* Can the second half be done first?

2018-12-26T22:50:10Z

Second half of linear algebra

← Older revision		Revision as of 22:50, 26 December 2018
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	* Norm		* Norm
	* Eigen stuff		* Eigen stuff
	* Determinants?		* Determinants? Trace?
	* Spectral theorem		* Spectral theorem
	* Singular value decomposition		* Singular value decomposition

2018-12-26T22:49:53Z

First half of linear algebra

← Older revision		Revision as of 22:49, 26 December 2018
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	==First half of linear algebra==		==First half of linear algebra==

	The point of the first half is to consider general linear transformations and classify them into injective/surjective/bijective. See [http://www.math.ucla.edu/~davidjekel/Linear_Algebra/Linear_Algebra_Equivalences.pdf this table].		The point of the first half is to consider general linear transformations (i.e. does not restrict to operators) and classify them into injective/surjective/bijective. See [http://www.math.ucla.edu/~davidjekel/Linear_Algebra/Linear_Algebra_Equivalences.pdf this table].

	Topics include:		Topics include:

2018-12-26T22:47:00Z

Second half of linear algebra

← Older revision		Revision as of 22:47, 26 December 2018
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	* Spectral theorem		* Spectral theorem
	* Singular value decomposition		* Singular value decomposition
			* Diagonalization
			* Orthogonality
			* Orthonormal bases
			* Orthogonal projection