Introduction to Linear Algebra is an academic book written by MIT lecturer Gilbert Strang. This book follows the tested direct and simple approach that has been used in the previous editions. Rather than boring students with an insipid approach, the book delves into the finer details of the subject so that students can understand the concepts more precisely. The book features ten chapters, and these are, Eigen Values and Eigen Vectors, Determinants, Orthogonality, Vector Spaces and Subspaces, Solving Linear Equations, Introduction to Vectors, Linear Transformations, Numerical Linear Algebra, Applications, and Complex Vectors and Matrices. It also presents various practical explanations, along with examples. This is the third edition of the book and the content has been revised from the previous editions. The book also consists of conceptual questions that are provided for review.
Born on November 27, 1934, in Chicago, Gilbert Strang is an American mathematician who is known for his textbooks in the subject. He has worked as a lecturer of Mathematics at MIT. He completed his undergraduate studies at MIT and was a Rhodes Scholar at Balliol College, Oxford. He received his PhD from the University of California, Los Angeles (UCLA), and has since then been teaching at MIT. Some of his famous books are- Linear Algebra and Its Applications, Engineering Mathematics: Linear Algebra and its Applications, Calculus, Introduction to Applied Mathematics, and Essays in Linear Algebra.
Table of contents
1. Introduction to Vectors: 1.1 Vectors and linear combinations
1.2 Lengths and dot products
1.3 Matrices
2. Solving Linear Equations: 2.1 Vectors and linear equations
2.2 The idea of elimination
2.3 Elimination using matrices
2.4 Rules for matrix operations
2.5 Inverse matrices
2.6 Elimination = factorization: A = LU
2.7 Transposes and permutations
3. Vector Spaces and Subspaces: 3.1 Spaces of vectors
3.2 The nullspace of A: solving Ax = 0
3.3 The rank and the row reduced form
3.4 The complete solution to Ax = b
3.5 Independence, basis and dimension
3.6 Dimensions of the four subspaces
4. Orthogonality: 4.1 Orthogonality of the four subspaces
4.2 Projections
4.3 Least squares approximations
4.4 Orthogonal bases and Gram-Schmidt
5. Determinants: 5.1 The properties of determinants
5.2 Permutations and cofactors
5.3 Cramer's rule, inverses, and volumes
6. Eigenvalues and Eigenvectors: 6.1 Introduction to eigenvalues
6.2 Diagonalizing a matrix
6.3 Applications to differential equations
6.4 Symmetric matrices
6.5 Positive definite matrices
6.6 Similar matrices
6.7 Singular value decomposition (SVD)
7. Linear Transformations: 7.1 The idea of a linear transformation
7.2 The matrix of a linear transformation
7.3 Diagonalization and the pseudoinverse
8. Applications: 8.1 Matrices in engineering
8.2 Graphs and networks
8.3 Markov matrices, population, and economics
8.4 Linear programming
8.5 Fourier series: linear algebra for functions
8.6 Linear algebra for statistics and probability
8.7 Computer graphics
9. Numerical Linear Algebra: 9.1 Gaussian elimination in practice
9.2 Norms and condition numbers
9.3 Iterative methods for linear algebra
10. Complex Vectors and Matrices: 10.1 Complex numbers
10.2 Hermitian and unitary matrices
10.3 The fast Fourier transform
Solutions to selected exercises
Matrix factorizations
Conceptual questions for review
Glossary: a dictionary for linear algebra
Index
Teaching codes.
| Publisher | Wellesley Cambridge Press |
| Publication Year | 2009 |
| ISBN-13 | 9788175968110 |
| ISBN-10 | 8175968117 |
| Edition | 4th |
| Binding | Paperback |
| Number of Pages | 574 Pages |
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