This book is for junior/senior-level first courses in linear algebra and assumes calculus as a prerequisite.
This thorough and accessible text, from one of the leading figures in the use of technology in linear algebra, gives students a challenging and broad understanding of the subject. The author infuses key concepts with their modern practical applications to offer students examples of how mathematics is used in the real world. Each chapter contains integrated worked examples and chapter tests. The book stresses the important roles geometry and visualisation play in understanding linear algebra.
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ISBN-13
978-1-292-35487-3 (9781292354873)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Matrices and Systems of Equations?
1.1 Systems of Linear Equations?
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 Elementary Matrices
1.6 Partitioned Matrices
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Determinants
2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 Additional Topics and Applications
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Vector Spaces
3.1 Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Linear Transformations
4.1 Definition and Examples
4.2 Matrix Representations of Linear Transformations
4.3 Similarity
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Orthogonality
5.1 The Scalar Product in Rn
5.2 Orthogonal Subspaces
5.3 Least Squares Problems
5.4 Inner Product Spaces
5.5 Orthonormal Sets
5.6 The Gram-Schmidt Orthogonalization Process
5.7 Orthogonal Polynomials
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Eigenvalues
6.1 Eigenvalues and Eigenvectors
6.2 Systems of Linear Differential Equations
6.3 Diagonalization
6.4 Hermitian Matrices
6.5 The Singular Value Decomposition
6.6 Quadratic Forms
6.7 Positive Definite Matrices
6.8 Nonnegative Matrices
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Numerical Linear Algebra
7.1 Floating-Point Numbers
7.2 Gaussian Elimination
7.3 Pivoting Strategies
7.4 Matrix Norms and Condition Numbers
7.5 Orthogonal Transformations
7.6 The Eigenvalue Problem
7.7 Least Squares Problems
7.8 Iterative Methods
MATLAB Exercises
Chapter Test A: True or False
Chapter Test B
Canonical Forms
8.1 Nilpotent Operators
8.2 The Jordan Canonical Form
Appendix: MATLAB Bibliography Answers to Selected Exercises Index
