A Short Course in Matrix Theory

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Nova Publishers, 1997 - Mathematics - 158 pages
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Presents the essentials of matrix theory and linear algebra as quickly and painlessly as possible, with the intent of reaching the topics of eigenvalues, eigenvectors, diagonalization, and some applications within the time constraints of a short course. Concepts and techniques are introduced by exam
 

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Contents

Introduction
1
Vectors and Matrices
3
Section 12 Vectors
7
Section 13 Reduced Row Echelon Form
12
Section 14 Inverse
21
Section 15 Rank and Dimension
27
Section 16 Null Space and Hermite Form
33
Determinants
39
Applications
83
Section 42 Differential Equations
91
Section 43 Powers of a Matrix and the Fibonacci Sequence
96
Section 44 Least Squares Approximation
99
Geometry
103
Section 52 Lines in R
107
Section 53 Projection
113
Section 54 Orthogonal Matrices and Quadrics
115

Section 22 Applications of Determinant
47
Diagonalization
51
Section 32 Diagonalization
59
Section 33 Orthogonal Basis
66
Section 34 Orthogonal Diagonalization
73
Change of Basis
123
Answers to Selected Exercises
129
MATS
149
Index
157
Copyright

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Page 4 - This means that the number of columns of A must equal the number of rows of B.
Page 4 - The Kronecker product of two matrices A and B is denoted by A B and is computed in MATLAB by the command kron(A,B).

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