Linear Algebra 568 Fully Solved Problems

ISBN-10: 0071794565
ISBN-13: 9780071794565
Edition: 5th 2013
List price: $23.00 Buy it from $7.98
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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  More...

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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: 1.430
Language: English

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, advanced engineering, quantitative analysisSupports all the major textbooks for the linear algebra course

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

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