Linear Algebra with Maple
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- Wiley
More About This Title Linear Algebra with Maple
English
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
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
