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Advanced linear algebra / Bruce N. Cooperstein, University of California, Santa Cruz, USA

Author
Cooperstein, Bruce, 1950-
Published
Boca Raton : CRC Press, Taylor & Francis Group, [2015]
Edition
Second edition.
Physical Description
594 pages : illustrations ; 23 cm.

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Contents
Machine generated contents note: 1.Vector Spaces -- 1.1.Fields -- 1.2.The Space Fn -- 1.3.Vector Spaces over an Arbitrary Field -- 1.4.Subspaces of Vector Spaces -- 1.5.Span and Independence -- 1.6.Bases and Finite-Dimensional Vector Spaces -- 1.7.Bases and Infinite-Dimensional Vector Spaces -- 1.8.Coordinate Vectors -- 2.Linear Transformations -- 2.1.Introduction to Linear Transformations -- 2.2.The Range and Kernel of a Linear Transformation -- 2.3.The Correspondence and Isomorphism Theorems -- 2.4.Matrix of a Linear Transformation -- 2.5.The Algebra of L(V, W) and Mmn(F) -- 2.6.Invertible Transformations and Matrices -- 3.Polynomials -- 3.1.The Algebra of Polynomials -- 3.2.Roots of Polynomials -- 4.Theory of a Single Linear Operator -- 4.1.Invariant Subspaces of an Operator -- 4.2.Cyclic Operators -- 4.3.Maximal Vectors -- 4.4.Indecomposable Linear Operators -- 4.5.Invariant Factors and Elementary Divisors -- 4.6.Canonical Forms -- 4.7.Operators on Real and Complex Vector Spaces -- 5.Normed and Inner Product Spaces -- 5.1.Inner Products -- 5.2.Geometry in Inner Product Spaces -- 5.3.Orthonormal Sets and the Gram-Schmidt Process -- 5.4.Orthogonal Complements and Projections -- 5.5.Dual Spaces -- 5.6.Adjoints -- 5.7.Normed Vector Spaces -- 6.Linear Operators on Inner Product Spaces -- 6.1.Self-Adjoint and Normal Operators -- 6.2.Spectral Theorems -- 6.3.Normal Operators on Real Inner Product Spaces -- 6.4.Unitary and Orthogonal Operators -- 6.5.Polar and Singular Value Decomposition -- 7.Trace and Determinant of a Linear Operator -- 7.1.Trace of a Linear Operator -- 7.2.Determinant of a Linear Operator and Matrix -- 7.3.Uniqueness of the Determinant of a Linear Operator -- 8.Bilinear Forms -- 8.1.Basic Properties of Bilinear Maps -- 8.2.Symplectic Spaces -- 8.3.Quadratic Forms and Orthogonal Space -- 8.4.Orthogonal Space, Characteristic Two -- 8.5.Real Quadratic Forms -- 9.Sesquilinear Forms and Unitary Geometry -- 9.1.Basic Properties of Sesquilinear Forms -- 9.2.Unitary Space -- 10.Tensor Products -- 10.1.Introduction to Tensor Products -- 10.2.Properties of Tensor Products -- 10.3.The Tensor Algebra -- 10.4.The Symmetric Algebra -- 10.5.The Exterior Algebra -- 10.6.Clifford Algebras, char F [≠] 2 -- 11.Linear Groups and Groups of Isometries -- 11.1.Linear Groups -- 11.2.Symplectic Groups -- 11.3.Orthogonal Groups, char F [≠] 2 -- 11.4.Unitary Groups -- 12.Additional Topics in Linear Algebra -- 12.1.Matrix Norms -- 12.2.The Moore-Penrose Inverse of a Matrix -- 12.3.Nonnegative Matrices -- 12.4.The Location of Eigenvalues -- 12.5.Functions of Matrices -- 13.Applications of Linear Algebra -- 13.1.Least Squares -- 13.2.Error Correcting Codes -- 13.3.Ranking Webpages for Search Engines.
Subject(s)
Genre(s)
ISBN
9781482248845 (hbk.)
1482248840 (hbk.)
Note
"A Chapman and Hall book."
Bibliography Note
Includes bibliographical references (pages 587-588) and index.
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