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More copies of this ISBNOther titles in the Featured Titles for Linear Algebra series:Linear Algebraby Stephen H. Friedberg
Synopses & ReviewsPublisher Comments:For courses in Advanced Linear Algebra. This topselling, theoremproof text presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinitedimensional case where appropriate.  NEW  Added section on the singular value decomposition.  Discusses the pseudoinverse of a matrix or a linear transformation between finitedimensional inner product spaces.  NEW  Revised proofs, added examples and exercises.  Improves the clarity of the text and enhances students understanding of it.  Numerous accessible exercises  Enriches and extends the text material.  Offers students a chance to test their understanding by working interesting problems at a reasonable level of difficulty.  Realworld applications throughout.  Reveals to students the power of the subject by demonstrating its practical uses.
Synopsis: This topselling, theoremproof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinitedimensional case where appropriate. Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms. For statisticians and engineers.
Table of Contents1. 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 CayleyHamilton Theorem.
6. Inner Product Spaces.
Inner Products and Norms. The GramSchmidt Orthogonalization Process and Orthogonal Complements. The Adjoint of a Linear Operator. Normal and SelfAdjoint Operators. Unitary and Orthogonal Operators and Their Matrices. Orthogonal Projections and the Spectral Theorem. The Singular Value Decomposition and the Pseudoinverse. Bilinear and Quadratic Forms. Einstein's Special Theory of Relativity. Conditioning and the Rayleigh Quotient. The Geometry of Orthogonal Operators.
7. Canonical Forms.
The Jordan Canonical Form I. The Jordan Canonical Form II. The Minimal Polynomial. Rational Canonical Form.
Appendices.
Sets. Functions. Fields. Complex Numbers. Polynomials.
Answers to Selected Exercises.
Index. What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Related SubjectsScience and Mathematics » Mathematics » Algebra » General Science and Mathematics » Mathematics » Algebra » Linear Algebra 

