| I.Matrices, Arrays and Determinants 1.Linear algebra 2.Representation by ordered sets 3.Total matric algebra 4.Diagonal and scalar matrices 5.Transpose.Symmetric and skew matrices 6.Determinants 7.Properties of determinants 8.Rank and nullity 9.Identities among minors 10.Reducibility 11.Arrays and determinants of higher dimension 12.Matrices in non.commutative systems II.The characteristic equation 13.The minimum equation 14.The characteristic equation 15.Determination of the minimum equation 16.Characteristic roots 17.Conjugate sets 18.Limits for the characteristic roots 19.Characteristic roots of unitary matrices IlI.Associated Integral Matrices 20.Matrices with elements in a principal ideal ring 21.Construction of unimodular matrices 22.Associated matrices 23.Greatest common divisors 24.Linear form moduls 25.Ideals IV.Equivalence 26.Equivalent matrices 27.Invariant factors and elementary divisors 28.Factorization of a matrix 29.Polynomial domains 30.Equivalent pairs of matrices 31.Automorphic transformations V.Congruence 32.Matrices with elements in a principal ideal ring 33.Matrices with rational integral elements 34.Matrices with elements in a field 35.Matrices in an algebraically closed field 36.Hermitian matrices 37.Automorphs VI.Similarity 38.Similar matrices 39.Matrices with elements in a field 40.WEYR'S characteristic 4t.Unitary and orthogonal equivalence 42.The structure of unitary and orthogonal matrices VII.Composition of matrices 43.Direct sum and direct product 44.Product.matrices and power.matrices 45.Adjugates VIII.Matric equations 46.The general linear equation 47.Scalar equations 48.The unilateral equation IX.Functions of Matrices 49.Power series in matrices 50.Functions of matrices 51.Matrices whose elements are functions of complex variables 52.Derivatives and integrals of matrices X.Matrices of infinite order 53.Infinite determinants 54.Infinite matrices 55.A matric algebra of infinite order 50.Bounded matrices 57.Matrices with a non.denumerable number of rows and colums |
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