An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 193
... nxn matrices whose diagonal elements are identical except possibly for order . Show that there exists a non - singular symmetric matrix H such that HAH B. = 8. Show that the reduction to normal form of an mxn matrix can always be ...
... nxn matrices whose diagonal elements are identical except possibly for order . Show that there exists a non - singular symmetric matrix H such that HAH B. = 8. Show that the reduction to normal form of an mxn matrix can always be ...
Page 271
... nxn matrices . The proof of Theorem 9.3.2 not merely establishes the existence of a matrix representation for every finite group but describes an actual procedure for constructing such a representation . In particular , it provides a ...
... nxn matrices . The proof of Theorem 9.3.2 not merely establishes the existence of a matrix representation for every finite group but describes an actual procedure for constructing such a representation . In particular , it provides a ...
Page 430
... nxn matrix A , Σ det ( I + DA ) = 2n - 1 ( 1 + det A ) , where the summation extends over all matrices D in D. 26. Let n > 3. Let A1 , ... , A , be n × n matrices such that A1 ... An = I , | A1 | = = | An = - 1 , and A ̧ - Ax ( 2 ≤ k ...
... nxn matrix A , Σ det ( I + DA ) = 2n - 1 ( 1 + det A ) , where the summation extends over all matrices D in D. 26. Let n > 3. Let A1 , ... , A , be n × n matrices such that A1 ... An = I , | A1 | = = | An = - 1 , and A ̧ - Ax ( 2 ≤ k ...
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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Expressions et termes fréquents
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