Linear Algebra 568 Fully Solved Problems

Name: Linear Algebra 568 Fully Solved Problems
Price: 6.13 USD
Availability: InStock
ISBN: 9780071794565

ISBN-10: 0071794565

ISBN-13: 9780071794565

Edition: 5th 2013

Authors: Seymour Lipschutz, Marc Lipson

List price: $23.00

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Description:

The ideal review for your linear algebra courseMore than 40 million students have trusted Schaum’s Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in this field,Schaum's Outline of Linear Algebracovers what you need to know for your course and, more important, your exams. Step-by-step, the authors walk you through coming up with solutions to exercises in this topic.Outline format supplies a concise guide to the standard college course568 problems solved step-by-stepClear, concise explanations of all linear algebra conceptsAppropriate for the following courses: beginning linear algebra, linear algebra, advanced linear algebra, advanced physics,…

Book details

List price: $23.00
Edition: 5th
Copyright year: 2013
Publisher: McGraw-Hill Companies, The
Publication date: 12/11/2012
Binding: Paperback
Pages: 432
Size: 8.00" wide x 10.50" long x 1.00" tall
Weight: 1.628
Language: English

Marc Lipson, Ph.D. (Philadelphia, PA), is on the mathematical faculty of the University of Georgia. He is co-author of Schaum's Outline of Discrete Mathematics.



List of Symbols



Vectors in R<sup>n</sup> and C<sup>n</sup>, Spatial Vectors



Introduction



Vectors in R<sup>n</sup>



Vector Addition and Scalar Multiplication



Dot (Inner) Product



Located Vectors, Hyperplanes, Lines, Curves in R<sup>n</sup>



Vectors in R<sup>3</sup> (Spatial Vectors), ijk Notation



Complex Numbers



Vectors in C<sup>n</sup>



Algebra of Matrices



Introduction



Matrices



Matrix Addition and Scalar Multiplication



Summation Symbol



Matrix Multiplication



Transpose of a Matrix



Square Matrices



Powers of Matrices, Polynomials in Matrices



Invertible (Nonsingular) Matrices



Special Types of Square Matrices



Complex Matrices



Block Matrices



Systems of Linear Equations



Introduction



Basic Definitions, Solutions



Equivalent Systems, Elementary Operations



Small Square Systems of Linear Equations



Systems in Triangular and Echelon Forms



Gaussian Elimination



Echelon Matrices, Row Canonical Form, Row Equivalence



Gaussian Elimination, Matrix Formulation



Matrix Equation of a System of Linear Equations



Systems of Linear Equations and Linear Combinations of Vectors



Homogeneous Systems of Linear Equations



Elementary Matrices



LU Decomposition



Vector Spaces



Introduction



Vector Spaces



Examples of Vector Spaces



Linear Combinations, Spanning Sets



Subspaces



Linear Spans, Row Space of a Matrix



Linear Dependence and Independence



Basis and Dimension



Application to Matrices, Rank of a Matrix



Sums and Direct Sums



Coordinates



Linear Mappings



Introduction



Mappings, Functions



Linear Mappings (Linear Transformations)



Kernel and Image of a Linear Mapping



Singular and Nonsingular Linear Mappings, Isomorphisms



Operations with Linear Mappings



Algebra A(V) of Linear Operators



Linear Mappings and Matrices



Introduction



Matrix Representation of a Linear Operator



Change of Basis



Similarity



Matrices, and General Linear Mappings



Inner Product Spaces, Orthogonality



Introduction



Inner Product Spaces



Examples of Inner Product Spaces



Cauchy-Schwarz Inequality, Applications



Orthogonality



Orthogonal Sets and Bases



Gram-Schmidt Orthogonalization Process



Orthogonal and Positive Definite Matrices



Complex Inner Product Spaces



Normed Vector Spaces (Optional)



Determinants



Introduction



Determinants of Orders 1 and 2



Determinants of Order 3



Permutations



Determinants of Arbitrary Order



Properties of Determinants



Minors and Cofactors



Evaluation of Determinants



Classical Adjoint



Applications to Linear Equations, Cramer's Rule



Submatrices, Minors, Principal Minors



Block Matrices and Determinants



Determinants and Volume



Determinant of a Linear Operator



Multilinearity and Determinants



Diagonalization: Eigenvalues and Eigenvectors



Introduction



Polynomials of Matrices



Characteristic Polynomial, Cayley-Hamilton Theorem



Diagonalization, Eigenvalues and Eigenvectors



Computing Eigenvalues and Eigenvectors, Diagonalizing Matrices



Diagonalizing Real Symmetric Matrices and Quadratic Forms



Minimal Polynomial



Characteristic and Minimal Polynomials of Block Matrices



Canonical Forms



Introduction



Triangular Form



Invariance



Invariant Direct-Sum Decompositions



Primary Decomposition



Nilpotent Operators



Jordan Canonical Form



Cyclic Subspaces



Rational Canonical Form



Quotient Spaces



Linear Functionals and the Dual Space



Introduction



Linear Functionals and the Dual Space



Dual Basis



Second Dual Space



Annihilators



Transpose of a Linear Mapping



Bilinear, Quadratic, and Hermitian Forms



Introduction



Bilinear Forms



Bilinear Forms and Matrices



Alternating Bilinear Forms



Symmetric Bilinear Forms, Quadratic Forms



Real Symmetric Bilinear Forms, Law of Inertia



Hermitian Forms



Linear Operators on Inner Product Spaces



Introduction



Adjoint Operators



Analogy Between A(V) and C, Special Linear Operators



Self-Adjoint Operators



Orthogonal and Unitary Operators



Orthogonal and Unitary Matrices



Change of Orthonormal Basis



Positive Definite and Positive Operators



Diagonalization and Canonical Forms in Inner Product Spaces



Spectral Theorem



Multilinear Products



Algebraic Structures



Polynomials over a Field



Odds and Ends


Index