Description: Preface 1. Systems of Equations * Solutions of systems of equations 2. Augmented Matrices and Elementary Row Operations * Augmented matrix * Elementary row operation * Echelon form * Reduced echelon form * Gauss-Jordan elimination * Transpose * Rank 3. The Algebra of Matrices * Matrix addition * Scalar multiplication * Matrix multiplication 4. Inverses of Matrices * Matrix inversion 5. Determinants, Adjoints, and Cramer's Rule * Determinant * Adjoint * Cramer's rule 6. Application: Matrix Algebra and Modular Arithmetic * Modular arithmetic * Matrix operations * Hill codes 7. Vector Products, Lines, and Planes * Dot product * Cross product * Projection * Unit vector * Vectors in R'n * Orthogonal vectors 8. Vector Spaces and Subspaces * Vector space * Subspace * Spaces of functions and matrices * Linear combination * Spanning Set * Null Space * Rank of a matrix 9. Independence, Basis and Dimension * Linearly independent set * Basis * Dimension * Coordinate vector 10. Row Space, Column Space, and Null Space * Row space * Column space * Null space * Rank * Nullity 11. Inner Product Spaces * General inner products 12. Orthonormal Bases and the Gram-Schmidt Process * Orthonormal basis * Gram-Schmidt process 13. Change of Basis and Orthogonal Matrices * Transition (or change of basis) matrix * Orthogonal matrices 14. Eigenvalues and Eigenvectors * Characteristic polynomial * Eigenvalue * Eigenvector * Eigenspace 15. Diagonalization and Orthogonal Diagonalization * Similarity * Diagonalization * Symmetric matrix * Orthogonal diagonalization 16. Matrices and Linear Transformations from R'm to R'n * Linear transformation * Matrix of a linear transformation * Kernel of a linear transformation * Image of a linear transformation * Inverse of a linear transformation * Composition of linear transformations 17. Matrices of General Linear Transformations; Similarity * Matrix of a linear transformation * Similar matrices 18. Applications and Numerical Methods * Systems of differential equations * Gauss-Seidel method * Generalized inverse and curve fitting * Rotation of axes * LU and QR factorizations Appendix A. Maple V Mini-Reference Appendix B. User-Defined Functions

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