1. Matrices andSystems of Equations
1.1 Systems of LinearEquations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 ElementaryMatrices
1.6 PartitionedMatrices
MATLAB Exercises
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2. Determinants
2.1 The Determinantof a Matrix
2.2 Properties ofDeterminants
2.3 Additional Topicsand Applications
MATLAB Exercises
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Chapter Test B
3. Vector Spaces
3.1 Definition andExamples
3.2 Subspaces
3.3 LinearIndependence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space andColumn Space
MATLAB Exercises
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Chapter Test B
4. LinearTransformations
4.1 Definition andExamples
4.2 MatrixRepresentations of Linear Transformations
4.3 Similarity
MATLAB Exercises
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5. Orthogonality
5.1 The ScalarProduct in Rn
5.2 OrthogonalSubspaces
5.3 Least SquaresProblems
5.4 Inner ProductSpaces
5.5 Orthonormal Sets
5.6 The Gram–SchmidtOrthogonalization Process
5.7 OrthogonalPolynomials
MATLAB Exercises
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6. Eigenvalues
6.1 Eigenvalues andEigenvectors
6.2 Systems of LinearDifferential Equations
6.3 Diagonalization
6.4 HermitianMatrices
6.5 The SingularValue Decomposition
6.6 Quadratic Forms
6.7 Positive DefiniteMatrices
