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Linear Algebra, 3/E
Stephen H. Friedberg, Illinois State University
Arnold J. Insel, Illinois State University
Lawrence E. Spence, Illinois State University

ISBN-10: 0132338599
ISBN-13:  9780132338592

Publisher:  Pearson
Copyright:  1997
Format:  Cloth; 557 pp
Published:  08/22/1996


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Description

Appropriate for advanced first courses or regular second courses in linear algebra.

An accessible, applications-oriented presentation of the theory of linear algebra. This is the top selling theorem-proof text in the market.


Features

  • A significant number of interesting and accessible exercises. Pg.___
  • Real-world applications are provided throughout the book that reveal the power of the subject by demonstrating its practical uses. Pg.___
  • The text has been extensively rewritten with many additional examples and exercises and for increased clarity.
  • Additional material on the reduced echelon form of a matrix is included in Section 3.4.


New To This Edition

  • NEW—The text has been extensively rewritten with many additional examples and exercises and for increased clarity.
  • NEW—Additional material on the reduced echelon form of a matrix is included in Section 3.4.


Table of Contents



Preface.


1. Vector Spaces.

Introduction. Vector Spaces. Subspaces. Linear Combinations and Systems of Linear Equations. Linear Dependence and Linear Independence. Bases and Dimension. Maximal Linearly Independent Subsets.



2. Linear Transformations and Matrices.

Linear Transformations, Null Spaces, and Ranges. The Matrix Representation of a Linear Transformation. Composition of Linear Transformations and Matrix Multiplication. Invertibility and Isomorphisms. The Change of Coordinate Matrix. Dual Spaces. Homogeneous Linear Differential Equations with Constant Coefficients.



3. Elementary Matrix Operations and Systems of Linear Equations.

Elementary Matrix Operations and Elementary Matrices. The Rank of a Matrix and Matrix Inverses. Systems of Linear Equations—Theoretical Aspects. Systems of Linear Equations—Computational Aspects.



4. Determinants.

Determinants of Order 2. Determinants of Order n. Properties of Determinants. Summary—Important Facts about Determinants. A Characterization of the Determinant.



5. Diagonalization.

Eigenvalues and Eigenvectors. Diagonalizability. Matrix Limits and Markov Chains. Invariant Subspaces and the Cayley-Hamilton Theorem.



6. Inner Product Spaces.

Inner Products and Norms. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear Operator. Normal and Self-Adjoint Operators. Unitary and Orthogonal Operators and Their Matrices. Orthogonal Projections and the Spectral Theorem. Bilinear and Quadratic Forms. Einstein's Special Theory of Relativity. Conditioning and the Rayleigh Quotient. The Geometry of Orthogonal Operators.



7. Canonical Forms.

Jordan Canonical Form I. Jordan Canonical Form II. The Minimal Polynomial. Rational Canonical Form.



Appendices.

Sets. Functions. Fields. Complex Numbers. Polynomials.



Answers to Selected Exercises.


List of Frequently Used Symbols.


Index of Theorems.


Index.


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