Linear algebra

Title:

Linear algebra

Personal Author:

Lipschutz, Seymour.

Series:

Schaum's outlines.

Schaum's outline series.

Edition:

5th ed.

Publication Information:

New York ; London : McGraw-Hill, 2013.

Physical Description:

vi, 426 p. : ill. ; 28 cm.

ISBN:

9780071794565

General Note:

Previous ed.: 2011.

Includes index.

Subject Term:

Algebras, Linear -- Problems, exercises, etc.

Algebras, Linear -- Outlines, syllabi, etc.

Added Author:

Lipson, Marc.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... MJIIT Library	30000010240012	QA188 L57 2013 f	Open Access Book	Book	Searching... Unknown

Summary

Tough Test Questions? Missed Lectures? Not Enough Time?

Fortunately, there's Schaum's. This all-in-one-package includes 612 fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to build confidence, skills, and knowledge for the highest score possible.

More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

612 fully solved problems Concise explanations of all course concepts Support for all major textbooks for linear algebra courses

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Author Notes

Seymour Lipschutz is on the faculty of Temple University and formally taught at the Polytechnic Institute of Brooklyn. He is one of Schaum's major authors.
Marc Lipson is on the faculty of University of Georgia. He is also the coauthor of Schaum's Outline of Discrete Mathematics and Schaum's Outline of Probability with Seymour Lipschutz.

List of Symbols	p. iv
Chapter 1 Vectors in R n and C n , Spatial Vectors	p. 1
1.1 Introduction
1.2 Vectors in R n
1.3 Vector Addition and Scalar Multiplication
1.4 Dot (Inner) Product
1.5 Located Vectors, Hyperplanes, Lines, Curves in R n
1.6 Vectors in R 3 (Spatial Vectors), ijk Notation
1.7 Complex Numbers
1.8 Vectors in C n
Chapter 2 Algebra of Matrices	p. 27
2.1 Introduction
2.2 Matrices
2.3 Matrix Addition and Scalar Multiplication
2.4 Summation Symbol
2.5 Matrix Multiplication
2.6 Transpose of a Matrix
2.7 Square Matrices
2.8 Powers of Matrices, Polynomials in Matrices
2.9 Invertible (Nonsingular) Matrices
2.10 Special Types of Square Matrices
2.11 Complex Matrices
2.12 Block Matrices
Chapter 3 Systems of Linear Equations	p. 57
3.1 Introduction
3.2 Basic Definitions, Solutions
3.3 Equivalent Systems, Elementary Operations
3.4 Small Square Systems of Linear Equations
3.5 Systems in Triangular and Echelon Forms
3.6 Gaussian Elimination
3.7 Echelon Matrices, Row Canonical Form, Row Equivalence
3.8 Gaussian Elimination, Matrix Formulation
3.9 Matrix Equation of a System of Linear Equations
3.10 Systems of Linear Equations and Linear Combinations of Vectors
3.11 Homogeneous Systems of Linear Equations
3.12 Elementary Matrices
3.13 LU Decomposition
Chapter 4 Vector Spaces	p. 112
4.1 Introduction
4.2 Vector Spaces
4.3 Examples of Vector Spaces
4.4 Linear Combinations, Spanning Sets
4.5 Subspaces
4.6 Linear Spans, Row Space of a Matrix
4.7 Linear Dependence and Independence
4.8 Basis and Dimension
4.9 Application to Matrices, Rank of a Matrix
4.10 Sums and Direct Sums
4.11 Coordinates
Chapter 5 Linear Mappings	p. 164
5.1 Introduction
5.2 Mappings, Functions
5.3 Linear Mappings (Linear Transformations)
5.4 Kernel and Image of a Linear Mapping
5.5 Singular and Nonsingular Linear Mappings, Isomorphisms
5.6 Operations with Linear Mappings
5.7 Algebra A(V) of Linear Operators
Chapter 6 Linear Mappings and Matrices	p. 195
6.1 Introduction
6.2 Matrix Representation of a Linear Operator
6.3 Change of Basis
6.4 Similarity
6.5 Matrices, and General Linear Mappings
Chapter 7 Inner Product Spaces, Orthogonality	p. 226
7.1 Introduction
7.2 Inner Product Spaces
7.3 Examples of Inner Product Spaces
7.4 Cauchy-Schwarz Inequality, Applications
7.5 Orthogonality
7.6 Orthogonal Sets and Bases
7.7 Gram-Schmidt Orthogonalization Process
7.8 Orthogonal and Positive Definite Matrices
7.9 Complex Inner Product Spaces
7.10 Normed Vector Spaces (Optional)
Chapter 8 Determinants	p. 264
8.1 Introduction
8.2 Determinants of Orders 1 and 2
8.3 Determinants of Order 3
8.4 Permutations
8.5 Determinants of Arbitrary Order
8.6 Properties of Determinants
8.7 Minors and Cofactors
8.8 Evaluation of Determinants
8.9 Classical Adjoint
8.10 Applications to Linear Equations, Cramer's Rule
8.11 Submatrices, Minors, Principal Minors
8.12 Block Matrices and Determinants
8.13 Determinants and Volume
8.14 Determinant of a Linear Operator
8.15 Multilinearity and Determinants
Chapter 9 Diagonalization: Eigenvalues and Eigenvectors	p. 292
9.1 Introduction
9.2 Polynomials of Matrices
9.3 Characteristic Polynomial, Cayley-Hamilton Theorem
9.4 Diagonalization, Eigenvalues and Eigenvectors
9.5 Computing Eigenvalues and Eigenvectors, Diagonalizing Matrices
9.6 Diagonalizing Real Symmetric Matrices and Quadratic Forms
9.7 Minimal Polynomial
9.8 Characteristic and Minimal Polynomials of Block Matrices
Chapter 10 Canonical Forms	p. 325
10.1 Introduction
10.2 Triangular Form
10.3 Invariance
10.4 Invariant Direct-Sum Decompositions
10.5 Primary Decomposition
10.6 Nilpotent Operators
10.7 Jordan Canonical Form
10.8 Cyclic Subspaces
10.9 Rational Canonical Form
10.10 Quotient Spaces
Chapter 11 Linear Functionals and the Dual Space	p. 349
11.1 Introduction
11.2 Linear Functionals and the Dual Space
11.3 Dual Basis
11.4 Second Dual Space
11.5 Annihilators
11.6 Transpose of a Linear Mapping
Chapter 12 Bilinear, Quadratic, and Hermitian Forms	p. 359
12.1 Introduction
12.2 Bilinear Forms
12.3 Bilinear Forms and Matrices
12.4 Alternating Bilinear Forms
12.5 Symmetric Bilinear Forms, Quadratic Forms
12.6 Real Symmetric Bilinear Forms, Law of Inertia
12.7 Hermitian Forms
Chapter 13 Linear Operators on Inner Product Spaces	p. 377
13.1 Introduction
13.2 Adjoint Operators
13.3 Analogy Between A(V) and C, Special Linear Operators
13.4 Self-Adjoint Operators
13.5 Orthogonal and Unitary Operators
13.6 Orthogonal and Unitary Matrices
13.7 Change of Orthonormal Basis
13.8 Positive Definite and Positive Operators
13.9 Diagonalization and Canonical Forms in Inner Product Spaces
13.10 Spectral Theorem
Appendix A Multilinear Products	p. 396
Appendix B Algebraic Structures	p. 403
Appendix C Polynomials over a Field	p. 411
Appendix D Odds and Ends	p. 415
Index	p. 422

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Summary

Summary

Author Notes

Table of Contents