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Introduction to matrix theory : with applications to business and economics /

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Bibliographic Details
Main Author: Szidarovszky, Ferenc (Author)
Other Authors: Molnár, Sándor, Dr
Format: Book
Language:English
Published: River Edge, N.J. : World Scientific, [2002]
Series:Series on concrete and applicable mathematics ; v. 3.
Subjects:
Matrices.
Matrices
Matrizentheorie
Online Access:Table of contents
Table of contents
Table of Contents:
  • Vectors and Matrices
  • Comparison of Matrices
  • Elementary Matrix Algebra
  • Inverse of a Matrix
  • Vector Spaces and Inner-Product Spaces
  • Subspaces
  • Linear Independence, Basis
  • Inner-Product Spaces
  • Direct Sums and Orthogonal Complementary Subspaces
  • Applications
  • Systems of Linear Equations and Inverses of Matrices
  • Existence and Uniqueness of a Solution
  • Systems of Homogeneous Linear Equations
  • Systems of Inhomogeneous Linear Equations
  • Rank of Matrices
  • Matrix Equations and Inverses of Matrices
  • The Elimination Method
  • Applications
  • Determinants
  • Properties of Determinants
  • Cofactors and Expansion by Cofactors
  • Determinants and Systems of Linear Equations
  • Further Examples and Applications
  • Linear Mappings and Matrices
  • Vector Coordinates
  • Linear Mappings
  • The Vector Space of Linear Mappings
  • Multiplication of Linear Mappings, and Inverses
  • Matrix Representations of Linear Mappings
  • Coordinates and Matrix Representation in a New Basis
  • Applications
  • Eigenvalues, Invariant Subspaces, Canonical Forms
  • Matrix Polynomials
  • The Construction of Invariant Subspaces
  • Diagonal and Triangular Forms
  • The Jordan Canonical Form
  • Complexification
  • Special Matrices
  • Diagonal, Tridiagonal, and Triangular Matrices
  • Idempotent and Nilpotent Matrices
  • Matrices in Inner Product Spaces
  • Definite Matrices
  • Nonnegative Matrices
  • Elements of Matrix Analysis
  • Vector Norms
  • Matrix Norms.