| Description |
xiii, 275 pages : illustrations ; 24 cm |
| Contents |
Machine derived contents note: 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 Rn - 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 Rm to Rn -- - 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 |
| Analysis |
Linear algebra Use of Computers |
| Bibliography |
Includes bibliographical references (pages 269-270) |
| SUBJECT |
Maple (Computer file) http://id.loc.gov/authorities/names/n88244754
|
| Subject |
Algebras, Linear -- Data processing.
|
| Author |
Evans, Benny.
|
|
Johnson, Jerry.
|
| LC no. |
95127133 |
| ISBN |
0471063681 |
|
