Math 570: Matrix Analysis - Revision history

Ls5: /* Catalog Information */

2023-04-10T13:27:39Z

‎Catalog Information

Ls5: moved Math 570 to Math 570: Matrix Analysis

2013-04-03T22:43:17Z

moved Math 570 to Math 570: Matrix Analysis

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2010-10-20T15:02:38Z

‎Minimal learning outcomes

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2010-10-19T19:33:45Z

‎Prerequisite

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2010-10-19T19:32:42Z

‎Courses for which this course is prerequisite

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2010-10-19T19:29:48Z

‎Minimal learning outcomes

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2010-10-19T19:28:53Z

‎Minimal learning outcomes

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2010-10-19T19:27:56Z

‎Additional topics

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2010-10-19T19:27:05Z

‎Minimal learning outcomes

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2010-10-19T19:23:23Z

‎Minimal learning outcomes

← Older revision		Revision as of 13:27, 10 April 2023
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	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	Winter (odd years) spring (even years)

	=== Prerequisite ===		=== Prerequisite ===

@@ Line 59: / Line 59: @@
 Positive and negative linear transformations,
 Fractional powers,
-Polar decompositions,
+Polar decompositions and applications,
-Applications,
 Singular value decomposition,
 The Frobenius norm and approximation in this norm,
@@ Line 68: / Line 67: @@
 The condition number,
 The spectral radius,
-Sequences and series of linear operators,
+Sequences and series of linear operators, Functions of linear transformations,
 Iterative methods for solutions of linear systems,

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 302]] or [[Math 313|313]]; or equivalents.
+[[Math 302]] or [[Math 313|313]]; or equivalents along with the undergraduate calculus sequence.
 === Description ===

← Older revision		Revision as of 19:32, 19 October 2010
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	=== Courses for which this course is prerequisite ===		=== Courses for which this course is prerequisite ===
		+
		+	None

	[[Category:Courses\|570]]		[[Category:Courses\|570]]

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 Eigenvalues and eigenvectors of linear transformations,
 Jordan Cannonical form and applications,
 Markov chains and migration processes,
 Regular Markov matrices,

← Older revision	Revision as of 22:43, 3 April 2013
(No difference)

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 === Additional topics ===
-Numerical methods for finding eigenvalues
+Numerical methods for finding eigenvalues,
-Power methods
+Power methods,
-The QR algorithm
+The QR algorithm,
-Rational canonical form
+Rational canonical form,
 === Courses for which this course is prerequisite ===
 [[Category:Courses|570]]

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 === Minimal learning outcomes ===
 <div style="-moz-column-count:2; column-count:2;">
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 </div>
-Matrix arithmetic and Linear transformations
+Matrix arithmetic and Linear transformations,
-The theory of determinants including all proofs of their properties
+The theory of determinants including all proofs of their properties,
-Rank of a matrix and elementary matrices
+Rank of a matrix and elementary matrices,
-Spectral theory
+Spectral theory,
-Shur's theorem
+Shur's theorem,
-Principal invariants of trace and determinant
+Principal invariants of trace and determinant,
-Quadratic forms and second derivative test
+Quadratic forms and second derivative test,
-Gerschgorin's theorem
+Gerschgorin's theorem,
-Abstract vector spaces and general fields
+Abstract vector spaces and general fields,
-Axioms
+Axioms,
-Subspaces and bases
+Subspaces and bases,
-Applications to general fields
+Applications to general fields,
-Linear transformations
+Linear transformations,
-Matrix of a linear transformation
+Matrix of a linear transformation,
-Rotations
+Rotations,
-Eigenvalues and eigenvectors of linear transformations
+Eigenvalues and eigenvectors of linear transformations,
-Cannonical forms
+Cannonical forms,
-Jordan Cannonical form
+Jordan Cannonical form,
-Markov chains and migration processes
+Markov chains and migration processes,
-Regular Markov matrices
+Regular Markov matrices,
-Absorbing states and gambler's ruin
+Absorbing states and gambler's ruin,
-Inner product spaces
+Inner product spaces,
-Gramm Schmidt process
+Gramm Schmidt process,
-Tensor product of vectors
+Tensor product of vectors,
-Least squares
+Least squares,
-Fredholm alternative
+Fredholm alternative,
-Determinants and volume
+Determinants and volume,
-Self adjoint operators
+Self adjoint operators,
-Simultaneous diagonalization
+Simultaneous diagonalization,
-Spectral theory of self adjoint operators
+Spectral theory of self adjoint operators,
-Positive and negative linear transformations
+Positive and negative linear transformations,
-Fractional powers
+Fractional powers,
-Polar decompositions
+Polar decompositions,
-Applications
+Applications,
-Singular value decomposition
+Singular value decomposition,
-The Frobenius norm and approximation in this norm
+The Frobenius norm and approximation in this norm,
-Least squares and the Moore Penrose inverse
+Least squares and the Moore Penrose inverse,
-Norms for finite dimensional vector spaces
+Norms for finite dimensional vector spaces,
-The p norms
+The p norms,
-The condition number
+The condition number,
-The spectral radius
+The spectral radius,
-Sequences and series of linear operators
+Sequences and series of linear operators,
-Iterative methods for solutions of linear systems
+Iterative methods for solutions of linear systems,
 === Textbooks ===