Introduction to Matrix Theory : With Applications to Business and Economics

by Szidarovszky, Ferenc; Molnar, Sandor

• ISBN13: 9789810245047
• ISBN10: 9810245041
• Format: Hardcover
• Copyright: 2002-08-01
• Publisher: World Scientific Pub Co Inc

Summary

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.

Table of Contents

Vectors and Matrices	1	(56)
Introduction	1	(6)
Comparison of Matrices	7	(1)
Elementary Matrix Algebra	8	(13)
Inverse of a Matrix	21	(3)
Further Examples and Applications	24	(28)
Exercises	52	(5)
Vector Spaces and Inner-Product Spaces	57	(76)
Introduction	57	(5)
Subspaces	62	(8)
Linear Independence, Basis	70	(15)
Inner-Product Spaces	85	(20)
Direct Sums and Orthogonal Complementary Subspaces	105	(14)
Applications	119	(8)
Exercises	127	(6)
Systems of Linear Equations and Inverses of Matrices	133	(74)
Introduction	133	(2)
Existence and Uniqueness of a Solution	135	(7)
Systems of Homogeneous Linear Equations	142	(7)
Systems of Inhomogeneous Linear Equations	149	(6)
Rank of Matrices	155	(2)
Matrix Equations and Inverses of Matrices	157	(8)
The Elimination Method	165	(23)
Applications	188	(12)
Exercises	200	(7)
Determinants	207	(44)
Introduction	207	(8)
Properties of Determinants	215	(10)
Cofactors and Expansion by Cofactors	225	(7)
Determinants and Systems of Linear Equations	232	(6)
Further Examples and Applications	238	(7)
Exercises	245	(6)
Linear Mappings and Matrices	251	(62)
Introduction	251	(1)
Vector Coordinates	251	(3)
Linear Mappings	254	(17)
The Vector Space of Linear Mappings	271	(2)
Multiplication of Linear Mappings, and Inverses	273	(11)
Matrix Representations of Linear Mappings	284	(9)
Coordinates and Matrix Representation in a New Basis	293	(6)
Applications	299	(7)
Exercises	306	(7)
Eigenvalues, Invariant Subspaces, Canonical Forms	313	(70)
Introduction	313	(1)
Basic Concepts	313	(12)
Matrix Polynomials	325	(11)
The Construction of Invariant Subspaces	336	(5)
Diagonal and Triangular Forms	341	(10)
The Jordan Canonical Form	351	(9)
Complexification	360	(1)
Applications	361	(17)
Exercises	378	(5)
Special Matrices	383	(72)
Introduction	383	(1)
Diagonal, Tridiagonal, and Triangular Matrices	383	(10)
Idempotent and Nilpotent Matrices	393	(3)
Matrices in Inner Product Spaces	396	(14)
Definite Matrices	410	(8)
Nonnegative Matrices	418	(19)
Applications	437	(13)
Exercises	450	(5)
Elements of Matrix Analysis	455	(40)
Introduction	455	(1)
Vector Norms	455	(6)
Matrix Norms	461	(13)
Applications	474	(17)
Exercises	491	(4)
References	495	(2)
Index	497