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Matrix Basics
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1
Matrix Operations
1.1
Matrix basics
1.1.1
Matrix size
1.1.2
Matrix elements
1.1.3
Matrix equality
1.1.4
Square matrix
1.1.5
Identity matrix
1.1.6
Zero matrix
1.2
Matrix operations
1.2.1
Matrix addition
1.2.2
Matrix-scalar multiplication
1.2.3
Matrix-matrix multiplication
1.3
Algebraic properties of matrix operations
1.3.1
Properties of matrix sum
1.3.2
Properties of matrix-scalar multiplication
1.3.3
Properties of matrix-matrix multiplication
1.4
Non-properties of matrices
1.5
Powers of matrices
1.5.1
Product of two powers
1.5.2
Power of a power
2
Matrix Transpose and Symmetric Matrices
2.1
The Transpose of a matrix
2.1.1
Properties of matrix transposes
2.2
Symmetric and skew-symmetric matrices
2.3
The trace of a matrix
2.3.1
Properties of the trace
3
Permutations and Elementary Matrices
3.1
Permutation matrices
3.2
Elementary matrices
3.2.1
Using elementary matrices
3.2.2
Row reduction with elementary matrices
3.2.3
Solving systems of equations with elimination matrices
4
Summary Types of Matrices
Chapter
4
Summary Types of Matrices
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