Contemporary Linear Algebra Book

Ch. 1	Vectors	1
1.1	Vectors and Matrices in Engineering and Mathematics; n-Space	1
1.2	Dot Product and Orthogonality	15
1.3	Vector Equations of Lines and Planes	29
Ch. 2	Systems of Linear Equations	39
2.1	Introduction to Systems of Linear Equations	39
2.2	Solving Linear Systems by Row Reduction	48
2.3	Applications of Linear Systems	63
Ch. 3	Matrices and Matrix Algebra	79
3.1	Operations on Matrices	79
3.2	Inverses; Algebraic Properties of Matrices	94
3.3	Elementary Matrices; A Method for Finding A[superscript -1]	109
3.4	Subspaces and Linear Independence	123
3.5	The Geometry of Linear Systems	135
3.6	Matrices with Special Forms	143
3.7	Matrix Factorizations; LU-Decomposition	154
3.8	Partitioned Matrices and Parallel Processing	166
Ch. 4	Determinants	175
4.1	Determinants; Cofactor Expansion	175
4.2	Properties of Determinants	184
4.3	Cramer's Rule; Formula for A[superscript -1]: Applications of Determinants	196
4.4	A First Look at Eigenvalues and Eigenvectors	210
Ch. 5	Matrix Models	225
5.1	Dynamical Systems and Markov Chains	225
5.2	Leontief Input-Output Models	235
5.3	Gauss-Seidel and Jacobi Iteration; Sparse Linear Systems	241
5.4	The Power Method; Application to Internet Search Engines	249
Ch. 6	Linear Transformations	265
6.1	Matrices as Transformations	265
6.2	Geometry of Linear Operators	280
6.3	Kernel and Range	296
6.4	Composition and Invertibility of Linear Transformations	305
6.5	Computer Graphics	318
Ch. 7	Dimension and Structure	329
7.1	Basis and Dimension	329
7.2	Properties of Bases	335
7.3	The Fundamental Spaces of a Matrix	342
7.4	The Dimension Theorem and Its Implications	352
7.5	The Rank Theorem and Its Implications	360
7.6	The Pivot Theorem and Its Implications	370
7.7	The Projection Theorem and Its Implications	379
7.8	Best Approximation and Least Squares	393
7.9	Orthonormal Bases and the Gram-Schmidt Process	406
7.10	QR-Decomposition; Householder Transformations	417
7.11	Coordinates with Respect to a Basis	426
Ch. 8	Diagonalization	443
8.1	Matrix Representations of Linear Transformations	443
8.2	Similarity and Diagonalizability	456
8.3	Orthogonal Diagonalizability; Functions of a Matrix	468
8.4	Quadratic Forms	481
8.5	Application of Quadratic Forms to Optimization	495
8.6	Singular Value Decomposition	502
8.7	The Pseudoinverse	518
8.8	Complex Eigenvalues and Eigenvectors	525
8.9	Hermitian, Unitary, and Normal Matrices	535
8.10	Systems of Differential Equations	542
Ch. 9	General Vector Spaces	555
9.1	Vector Space Axioms	555
9.2	Inner Product Spaces; Fourier Series	569
9.3	General Linear Transformations; Isomorphism	582
App. A	How to Read Theorems
App. B	Complex Numbers
	Answers to Odd-Numbered Exercises
	Photo Credits
	Index