TY - BOOK AU - Vatsa,B.S. AU - Vatsa,Suchi TI - Theory of Matrices SN - 9781781830529 AV - QA188 -- .V387 2013eb U1 - 512.9434 PY - 2012/// CY - Tunbridge Wells PB - New Academic Science KW - Matrices KW - Electronic books N1 - Cover -- Preface -- Contents -- Chapter 1 Matrices -- 1.1 Definition and Examples of a Matrix -- 1.2 Diagonal, Scalar,Unit, And Triangular Matrix -- 1.3 Equal and Unequal Matrices -- 1.4 The Transpose of a Matrix: Symmetric and Skew-Symmetric -- 1.5 The Conjugate of a Matrix: Hermitian and Skew-Hermitian Matrices -- 1.6 Submatrics -- Submatrices -- Chapter 2 Algebra of Matrices -- 2.1 Addition of Two Matrices -- 2.2 Properties of Addition -- 2.3 Scalar Multiples of Matrices -- 2.4 Multiplication of Matrices -- 2.5 The Properties of Matrix Multiplication -- 2.6 Powers of Matrices: Laws of Exponents -- 2.7. Idempotent, Nilpotent, Involutory, Orthogonal And Unitary Matrices -- Chapter 3 Determinants -- 3.1 Definition -- 3.2 Minors and Cofactors -- 3.3 Properties of Determinants -- 3.4 Laplace's Expansions -- 3.5 Symmetric and Skew-Symmetric Determinant -- 3.6 Product of Two Determinants -- 3.7 Reciprocal Determinant -- Chapter 4 Adjoint and Inverse of a Matrix -- 4.1 Definition and Examples -- 4.2 Inverse of a Matrix -- 4.3 Linear Computations -- 4.4 Partitioning of Matrices -- Chapter 5 Rank and Equivalence -- 5.1 The Concept of a Rank -- 5.2 Elementary Transformations -- 5.3 Equivalent Matrices -- 5.4 Elementary Matrices -- 5.5 Normal Form -- 5.6 Elementary Transformation by Matrix Multiplication -- 5.7 Computation of The Inverse of Matrix by Elementary Transformation -- Chapter 6 Linear Equations -- 6.1 System of Linear Equations and Consistency -- 6.2 Solution of n Linear Equations In n Unknowns -- 6.3 Solution of m Linear Equations In n Unknowns With m < -- n and m > -- n -- 6.4 Homogeneous Linear Equations -- Chapter 7 Vector Spaces and Linear Transformations -- 7.1 Definition of a Vector and Vector Spaces -- 7.2 Vector Space Spanned by a Given System of Vectors -- 7.3 Linearly Dependent and Linearly Independent System of Vectors; 7.4 Basis and Dimension -- 7.5 Subspace -- 7.6 Row and Column Space of a Matrix -- 7.7 Linear Transformations -- 7.8 Operators on Vnn -- 7.9 Geometric Transformation -- 7.10 Geometric Properties of Plane Linear Transformation -- 7.11 Rotation -- 7.12 Reflection -- 7.13 Expansions and Compressions -- 7.14 Shears -- 7.15 Translation -- 7.16 Successive Transformations -- 7.17 Inverse Transformation -- Chapter 8 Characteristic Roots and Vectors of a Matrix -- 8.1 Definition and Examples -- 8.2 Properties of The Characteristic Polynomial -- 8.3 Application of the Cayley-Hamilton Theorem In Finding Out The Inverse of a Non-Singular Matrix -- 8.4 The Minimum Polynomial of a Matrix -- 8.5 Characteristic Roots and Vectors of a Square Matrix -- 8.6 Characteristic Roots of Polynomial Function of a Matrix A -- 8.7 Characteristic Roots of Special Matrices -- 8.8 The Diagonal Form of a Hermitian Matrix -- Chapter 9 Bilinear Forms -- 9.1 Bilinear Forms -- 9.2 The Equivalence of Bilinear Forms -- 9.3 Types of Bilinear Forms -- 9.4 Cogredient Transformations -- 9.5 Contragredient Transformations -- Chapter 10 Quadratic Forms -- 10.1 Quadratic Forms -- 10.2 Linear Transformation -- 10.3 Reduction of Real Quadratic Form to Normal (or Canonical) Form -- 10.4 Lagrange's Reduction -- 10.5 Regular Quadratic Forms -- 10.6 Kronecker's Method of Reduction -- 10.7 Sylvester's Law of Inertia of Quadratic Forms -- 10.8 Definite, Semi-Definite and Indefinite Real Quadratic Forms -- 10.9 Definite Matrices -- 10.10 A Necessary and Sufficient Condition for Positive Definiteness -- Chapter 11 Hermitian Forms -- 11.1 Hermitian Forms -- 11.2 Definite Hermitian Form -- Chapter 12 Similar Matrices -- 12.1 Similar Matrices -- 12.2 Diagonal Matrices -- Answers to Problems -- Index UR - https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3440197 ER -