Introduction to Linear Algebra 5th Edition by Gilbert Strang 0980232775 9780980232776

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Product details:

• ISBN 10:0980232775

• ISBN 13:9780980232776 

• Author:Gilbert Strang 

 Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python.

Introduction to Linear Algebra 5th Table of contents:

1  Introduction

1.1  Vectors and Matrices
1.2  Lengths and Dot Products

   2  Solving Linear Equations

2.1  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  The Singular Value Decomposition

   7  Linear Transformations

7.1  The Idea of a Linear Transformation
7.2  The Matrix of a Linear Transformation
7.3  Change of Basis
7.4  Diagonalization and the Pseudoinverse

   8  Applications

8.1  Graphs and Networks
8.2  Markov Matrices and Economic Models
8.3  Linear Programming
8.4  Fourier Series: Linear Algebra for Functions
8.5  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 Complex Matrices

10.1 Complex Numbers
10.2 Hermitian and Unitary Matrices
10.3 The Fast Fourier Transform

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