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Linear Algebra With Applications

ISBN: 9780138493080 | 0138493081
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 8/1/1997

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SummaryTable of Contents
Renowned for its thoroughness and accessibility, this best-selling text by one of the leading figures in linear algebra reform offers students a challenging yet enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, it takes extra care in explaining concepts clearly so that students at a variety of levels can read and understand the material. Numerous worked examples are integrated throughout the text. This revision stresses the important roles played by geometry and visualization in linear algebra. ATLAST Computer Exercises for Linear Algebra a project manual using MATLAB--may be packaged free with the text.
1 MATRICES AND SYSTEMS OF EQUATIONS
1(83)
1 SYSTEMS OF LINEAR EQUATIONS
1(12)
2 ROW ECHELON FORM
... MORE
13(18)
3 MATRIX ALGEBRA
31(26)
4 ELEMENTARY MATRICES
57(11)
5 PARTITIONED MATRICES
68(9)
MATLAB EXERCISES
77(7)
2 DETERMINANTS
84(24)
1 THE DETERMINANT OF A MATRIX
84(8)
2 PROPERTIES OF DETERMINANTS
92(7)
3* CRAMER'S RULE
99(6)
MATLAB EXERCISES
105(3)
3 VECTOR SPACES
108(57)
1 DEFINITION AND EXAMPLES
108(8)
2 SUBSPACES
116(10)
3 LINEAR INDEPENDENCE
126(10)
4 BASIS AND DIMENSION
136(7)
5 CHANGE OF BASIS
143(10)
6 ROW SPACE AND COLUMN SPACE
153(8)
MATLAB EXERCISES
161(4)
4 LINEAR TRANSFORMATIONS
165(31)
1 DEFINITION AND EXAMPLES
165(10)
2 MATRIX REPRESENTATIONS OF LINEAR TRANSFORMATIONS
175(12)
3 SIMILARITY
187(7)
MATLAB EXERCISES
194(2)
5 ORTHOGONALITY
196(83)
1 THE SCALAR PRODUCT IN R(n)
197(11)
2 ORTHOGONAL SUBSPACES
208(8)
3 INNER PRODUCT SPACES
216(11)
4 LEAST SQUARES PROBLEMS
227(11)
5 ORTHONORMAL SETS
238(19)
6 THE GRAM-SCHMIDT ORTHOGONALIZATION PROCESS
257(9)
7* ORTHOGONAL POLYNOMIALS
266(8)
MATLAB EXERCISES
274(5)
6 EIGENVALUES
279(87)
1 EIGENVALUES AND EIGENVECTORS
280(12)
2 SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS
292(12)
3 DIAGONALIZATION
304(16)
4 HERMITIAN MATRICES
320(10)
5 QUADRATIC FORMS
330(14)
6 POSITIVE DEFINITE MATRICES
344(8)
7* NONNEGATIVE MATRICES
352(7)
8 MATLAB EXERCISES
359(7)
7 NUMERICAL LINEAR ALGEBRA
366(89)
1 FLOATING-POINT NUMBERS
367(4)
2 GAUSSIAN ELIMINATION
371(8)
3 PIVOTING STRATEGIES
379(6)
4 MATRIX NORMS AND CONDITION NUMBERS
385(13)
5 ORTHOGONAL TRANSFORMATIONS
398(11)
6 THE SINGULAR VALUE DECOMPOSITION
409(14)
7 THE EIGENVALUE PROBLEM
423(11)
8 LEAST SQUARES PROBLEMS
434(11)
MATLAB EXERCISES
445(10)
APPENDIX: MATLAB455(9)
BIBLIOGRAPHY464(2)
ANSWERS TO SELECTED EXERCISES466(19)
INDEX485

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