Matrix analysis and applied linear algebra. With solutions to problems

Carl D. Meyer9780898714548, 0898714540

Matrix Analysis and Applied Linear Algebra is an honest math text that circumvents the traditional definition-theorem-proof format that has bored students in the past. Meyer uses a fresh approach to introduce a variety of problems and examples ranging from the elementary to the challenging and from simple applications to discovery problems. The focus on applications is a big difference between this book and others. Meyer’s book is more rigorous and goes into more depth than some. He includes some of the more contemporary topics of applied linear algebra which are not normally found in undergraduate textbooks. Modern concepts and notation are used to introduce the various aspects of linear equations, leading readers easily to numerical computations and applications. The theoretical developments are always accompanied with examples, which are worked out in detail. Each section ends with a large number of carefully chosen exercises from which the students can gain further insight.
The textbook contains more than 240 examples, 650 exercises, historical notes, and comments on numerical performance and some of the possible pitfalls of algorithms. It comes with a solutions manual that includes complete solutions to all of the exercises. As a bonus, a CD-ROM is included that contains a searchable copy of the entire textbook and all solutions. Detailed information on topics mentioned in examples, references for additional study, thumbnail sketches and photographs of mathematicians, and a history of linear algebra and computing are also on the CD-ROM, which can be used on all platforms.
Students will love the book’s clear presentation and informal writing style. The detailed applications are valuable to them in seeing how linear algebra is applied to real-life situations. One of the most interesting aspects of this book, however, is the inclusion of historical information. These personal insights into some of the greatest mathematicians who developed this subject provide a spark for students and make the teaching of this topic more fun.

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Table of contents :
Matrix Analysis & Applied Linear Algebra……Page 1
Table of Contents……Page 2
Preface……Page 5
1.1 Introduction……Page 9
1.2 Gaussian Elimination & Matrices……Page 11
Solutions for exercises……Page 707
1.3 Gauss-Jordan Method……Page 23
Solutions for exercises……Page 708
1.4 Two-Point Boundary Value Problems……Page 26
1.5 Making Gaussian Elimination Work……Page 29
Solutions for exercises……Page 709
1.6 Ill-Conditioned Systems……Page 41
Solutions for exercises……Page 710
2.1 Row Echelon Form & Rank……Page 48
Solutions for exercises……Page 711
2.2 Reduced Row Echelon Form……Page 54
2.3 Consistency of Linear Systems……Page 60
Solutions for exercises……Page 712
2.4 Homogeneous Systems……Page 64
Solutions for exercises……Page 713
2.5 Nonhomogeneous Systems……Page 71
2.6 Electrical Circuits……Page 80
Solutions for exercises……Page 715
3.1 From Ancient China to Arthur Cayley……Page 85
3.2 Addition & Transposition……Page 87
Solutions for exercises……Page 717
3.3 Linearity……Page 95
3.4 Why do it This Way……Page 99
Solutions for exercises……Page 719
3.5 Matrix Multiplication……Page 101
3.6 Properties of Matrix Multiplication……Page 111
Solutions for exercises……Page 722
3.7 Matrix Inversion……Page 121
Solutions for exercises……Page 724
3.8 Inverses of Sums & Sensitivity……Page 130
Solutions for exercises……Page 725
3.9 Elementary Matrices & Equivalence……Page 137
Solutions for exercises……Page 727
3.10 The LU Factorization……Page 147
Solutions for exercises……Page 729
4.1 Spaces & Subspaces……Page 164
Solutions for exercises……Page 733
4.2 Four Fundalmental Subspaces……Page 174
Solutions for exercises……Page 735
4.3 Linear Independence……Page 186
Solutions for exercises……Page 736
4.4 Basis & Dimension……Page 199
Solutions for exercises……Page 739
4.5 More about Rank……Page 215
Solutions for exercises……Page 743
4.6 Classical Least Squares……Page 228
Solutions for exercises……Page 747
4.7 Linear Transformation……Page 243
Solutions for exercises……Page 748
4.8 Change of Basis and Similarity……Page 256
Solutions for exercises……Page 752
4.9 Invariant Subspaces……Page 264
Solutions for exercises……Page 754
5.1 Vector Norms……Page 273
Solutions for exercises……Page 757
5.2 Matrix Norms……Page 283
Solutions for exercises……Page 759
5.3 Inner-Product Spaces……Page 290
Solutions for exercises……Page 761
5.4 Orthogonal Vectors……Page 298
Solutions for exercises……Page 763
5.5 Gram–Schmidt Procedure……Page 311
Solutions for exercises……Page 766
5.6 Unitary & Orthogonal Matrices……Page 324
Solutions for exercises……Page 770
5.7 Orthogonal Reduction……Page 345
Solutions for exercises……Page 774
5.8 Dicrete Fourier Transform……Page 360
Solutions for exercises……Page 777
5.9 Complementary Subspaces……Page 387
Solutions for exercises……Page 787
5.10 Range-Nullspace Decomposition……Page 398
Solutions for exercises……Page 795
5.11 Orthogonal Decomposition……Page 407
Solutions for exercises……Page 799
5.12 Singular Value Decomposition……Page 415
Solutions for exercises……Page 803
5.13 Orthogonal Projection……Page 433
Solutions for exercises……Page 809
5.14 Why Least Squares……Page 450
Solutions for exercises……Page 817
5.15 Angles between Subspaces……Page 454
Solutions for exercises……Page 818
6.1 Determinants……Page 463
Solutions for exercises……Page 821
6.2 Additional Properties of Determinants……Page 479
Solutions for exercises……Page 824
7.1 Elementary Properties of Eigensystems……Page 492
Solutions for exercises……Page 831
7.2 Diagonalization by Similarity Transformations……Page 508
Solutions for exercises……Page 837
7.3 Functions of Diagonalization Matrices……Page 528
Solutions for exercises……Page 843
7.4 Systems of Differential Equations……Page 544
Solutions for exercises……Page 847
7.5 Normal Matrices……Page 550
Solutions for exercises……Page 849
7.6 Positive Definite Matrices……Page 561
Solutions for exercises……Page 851
7.7 Nilpotent Matrices & Jordan Structures……Page 577
Solutions for exercises……Page 854
7.8 Jordan Form……Page 590
Solutions for exercises……Page 856
7.9 Functions of Nondiagonalizable Matrices……Page 602
Solutions for exercises……Page 859
7.10 Difference Equations, Limits, & Summability……Page 619
Solutions for exercises……Page 864
7.11 Minimum Polunomials & Krylov Methods……Page 645
Solutions for exercises……Page 871
8.1 Introduction……Page 664
8.2 POSITIVE MATRICES……Page 666
Solutions for exercises……Page 872
8.3 Nonnegative Matrices……Page 673
Solutions for exercises……Page 873
8.4 Stochastic Matrices & Markov Chains……Page 690
Solutions for exercises……Page 875
Index……Page 877