Introduction To Matrix Theory

With Applications To Business And Economics

By: Sandor Molnar, Ferenc Szidarovszky

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Hardcover | 4 June 2002

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512 Pages

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In economic modeling and planning, as well as in business, most problems are linear, or approximated by linear models. Such problems are solved by matrix methods, so the material presented in this book is essential to these fields.

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Non-Fiction Mathematics Algebra Applied Mathematics Economics Economic Theory & Philosophy Booktopia Publisher Services World Scientific Publishing

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Published: 4th June 2002

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Vectors and Matrices	p. 1
Introduction	p. 1
Comparison of Matrices	p. 7
Elementary Matrix Algebra	p. 8
Inverse of a Matrix	p. 21
Further Examples and Applications	p. 24
Exercises	p. 52
Vector Spaces and Inner-Product Spaces	p. 57
Introduction	p. 57
Subspaces	p. 62
Linear Independence, Basis	p. 70
Inner-Product Spaces	p. 85
Direct Sums and Orthogonal Complementary Subspaces	p. 105
Applications	p. 119
Exercises	p. 127
Systems of Linear Equations and Inverses of Matrices	p. 133
Introduction	p. 133
Existence and Uniqueness of a Solution	p. 135
Systems of Homogeneous Linear Equations	p. 142
Systems of Inhomogeneous Linear Equations	p. 149
Rank of Matrices	p. 155
Matrix Equations and Inverses of Matrices	p. 157
The Elimination Method	p. 165
Applications	p. 188
Exercises	p. 200
Determinants	p. 207
Introduction	p. 207
Properties of Determinants	p. 215
Cofactors and Expansion by Cofactors	p. 225
Determinants and Systems of Linear Equations	p. 232
Further Examples and Applications	p. 238
Exercises	p. 245
Linear Mappings and Matrices	p. 251
Introduction	p. 251
Vector Coordinates	p. 251
Linear Mappings	p. 254
The Vector Space of Linear Mappings	p. 271
Multiplication of Linear Mappings, and Inverses	p. 273
Matrix Representations of Linear Mappings	p. 284
Coordinates and Matrix Representation in a New Basis	p. 293
Applications	p. 299
Exercises	p. 306
Eigenvalues, Invariant Subspaces, Canonical Forms	p. 313
Introduction	p. 313
Basic Concepts	p. 313
Matrix Polynomials	p. 325
The Construction of Invariant Subspaces	p. 336
Diagonal and Triangular Forms	p. 341
The Jordan Canonical Form	p. 351
Complexification	p. 360
Applications	p. 361
Exercises	p. 378
Special Matrices	p. 383
Introduction	p. 383
Diagonal, Tridiagonal, and Triangular Matrices	p. 383
Idempotent and Nilpotent Matrices	p. 393
Matrices in Inner Product Spaces	p. 396
Definite Matrices	p. 410
Nonnegative Matrices	p. 418
Applications	p. 437
Exercises	p. 450
Elements of Matrix Analysis	p. 455
Introduction	p. 455
Vector Norms	p. 455
Matrix Norms	p. 461
Applications	p. 474
Exercises	p. 491
References	p. 495
Index	p. 497
Table of Contents provided by Syndetics. All Rights Reserved.

Introduction To Matrix Theory

With Applications To Business And Economics

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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