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Understanding More Linear Algebra
David Austin
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Front Matter
Colophon
Preface
1
Vector spaces
1.1
Vector spaces
1.1.1
Vector spaces
1.1.2
Linear combinations
1.1.3
Bases
1.2
Linear transformations
1.2.1
Linear transformations
1.2.2
The null space and range
1.2.3
Vector space isomorphisms
1.2.4
Representing linear transformations with matrices
1.3
Inner products
1.3.1
Inner products
1.3.2
Orthogonality
1.3.3
The adjoint of a linear transformation
1.4
The minimal polynomial
1.4.1
Properties of Polynomials
1.4.2
The minimal polynomial of an operator
2
Standard forms
2.1
Upper triangular matrices
2.1.1
Upper triangular matrices
2.2
The Spectral Theorem
2.2.1
The Schur decomposition
2.2.2
Self-adjoint operators
2.3
Nilpotent operators
2.3.1
Null spaces of powers
2.3.2
Nilpotent operators
2.4
Generalized eigenvectors
2.4.1
Generalized eigenvectors
2.4.2
Complex Vector Spaces
2.4.3
Jordan form
Backmatter
Colophon
Colophon
This book was authored in PreTeXt.