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Beattie C., Rossie J. Notes on matrix theory

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Beattie C., Rossie J. Notes on matrix theory
Department of Mathematics Virginia Tech, 2003. — 130 p.
Contents:
Linear equations and elementary matrix algebra { a review)1
Vectors in Rn and C n
Matrix Operations
Matrix Inverses
The LU Decomposition
Vector Spaces and Linear Transformations
Model for General Vector Spaces
The Basics of Bases
Spanning Sets and Linear Independence
Basis and Dimension
Change of Basis
Linear Transformations and their Representation
Matrix Representations
Similarity of Matrices
Determinants
Inner Products and Best Approximations
Inner Products
Best approximation and projections
Pseudoinverses
Orthonormal Bases and the QR Decomposition
Unitary Transformations and the Singular Value Decomposition
The Eigenvalue Problem
Eigenvalues and Eigenvectors
Eigenvalue Basics
The Minimal Polynomial
Invariant Subspaces and Jordan Forms
Invariant Subspaces
Jordan Forms
Diagonalization
The Schur Decomposition
Hermitian and other Normal Matrices
Hermitian matrices
Normal Matrices
Positive De nite Matrices
Revisiting the Singular Value Decomposition
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