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Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes give...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 1998. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/3435#t=toc |
| Summary: |
Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes given for the linear algebra course at the Department of Mathematics in Wuhan University. |
| Item Description: | Includes index. |
| Carrier Form: | 1 online resource (viii,444pages) : illustrations |
| ISBN: | 9789812817068 |
| Index Number: | QA184 |
| CLC: | O151.2 |
| Contents: | 1. Determinants. 1.1. Concept of determinants. 1.2. Basic properties of determinants. 1.3. Development of a determinant. 1.4. Cramer's theorem -- 2. Systems of linear equations. 2.1. Linear relations between vectors. 2.2. Systems of homogeneous linear equations. 2.3. Systems of fundamental solutions. 2.4. Systems of nonhomogeneous linear equations. 2.5. Elementary operations -- 3. Matrix operations. 3.1. Matrix addition and matrix multiplication. 3.2. Diagonal, symmetric, and orthogonal matrices. 3.3. Invertible matrices -- 4. Quadratic forms. 4.1. Standard forms of general quadratic forms. 4.2. Classification of real quadratic forms. 4.3. Bilinear forms -- 5. Matrices similar to diagonal matrices. 5.1. Eigenvalues and eigenvectors. 5.2. Diagonalization of matrices. 5.3. Diagonalization of real symmetric matrices. 5.4. Canonical form of orthogonal matrices. 5.5. Cayley-Hamilton theorem and minimum polynomials -- 6. Jordan canonical form of matrices. 6.1. Necessary and sufficient condition for two matrices to be similar. 6.2. Canonical form of A-matrices. 6.3. Necessary and sufficient condition for two A-matrices to be equivalent. 6.4. Jordan canonical forms -- 7. Linear spaces and linear transformations. 7.1. Concept of linear spaces. 7.2. Bases and coordinates. 7.3. Linear transformations. 7.4. Matrix representation of linear transformations. 7.5. Linear transformations from one linear space into another. 7.6. Dual spaces and dualistic transformations -- 8. Inner product spaces. 8.1. Concept of inner product spaces. 8.2. Orthonormal bases. 8.3. Orthogonal linear transformations. 8.4. Linear spaces over complex numbers with inner products. 8.5. Normal operators. |