An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 99
... functions of A. ( 3.7.7 ) DEFINITION 3.7.2 . Let f ( x ) , g ( x ) be scalar polynomials and let A be any square matrix such that | g ( A ) | ‡ 0. Then the matrix ... functions remains III , § 3.7 RATIONAL FUNCTIONS OF A SQUARE MATRIX 99.
... functions of A. ( 3.7.7 ) DEFINITION 3.7.2 . Let f ( x ) , g ( x ) be scalar polynomials and let A be any square matrix such that | g ( A ) | ‡ 0. Then the matrix ... functions remains III , § 3.7 RATIONAL FUNCTIONS OF A SQUARE MATRIX 99.
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Leonid Mirsky. THEOREM 3.7.3 . Any identity between scalar rational functions remains valid for the corresponding rational functions of a square matrix , provided that all the latter functions are defined . It is clearly sufficient to ...
Leonid Mirsky. THEOREM 3.7.3 . Any identity between scalar rational functions remains valid for the corresponding rational functions of a square matrix , provided that all the latter functions are defined . It is clearly sufficient to ...
Page 127
... function is denoted by N ( x ) or Nx , and is defined by the equation Ωχ = ao dnx dn - 1x - + α1 dtn din - 1 dx ・ + ... + an - 1 at + anx . It is clear that , for every real number a and every pair of functions x , y = C ( n ) , we ...
... function is denoted by N ( x ) or Nx , and is defined by the equation Ωχ = ao dnx dn - 1x - + α1 dtn din - 1 dx ・ + ... + an - 1 at + anx . It is clear that , for every real number a and every pair of functions x , y = C ( n ) , we ...
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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A₁ algebra assertion automorphism B₁ basis bilinear form bilinear operator canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix dimensionality E-operations equal equivalence EXERCISE exists follows functions given Hence hermitian form hermitian matrix identity implies inequality integers invariant space isomorphic linear equations linear manifold linear transformation linearly independent matrix group matrix of order minimum polynomial multiplication non-singular linear transformation non-singular matrix non-zero numbers nxn matrix obtain orthogonal matrix positive definite positive semi-definite possesses proof of Theorem prove quadratic form quadric rank relation represented respect result rotation S-¹AS satisfies scalar Show similar singular skew-symmetric matrix solution square matrix suppose symmetric matrix t₁ tion triangular unique unit element unitary matrix V₁ values vector space view of Theorem w₁ write x₁ xTAx y₁ zero