An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 208
... characteristic polynomial . Let A , ... , be the distinct characteristic roots of A , and denote their multiplicities by a , ... , a respectively , so that α1 , ... , α1 and a1 + ... CHARACTERISTIC EQUATION Estimates of characteristic roots.
... characteristic polynomial . Let A , ... , be the distinct characteristic roots of A , and denote their multiplicities by a , ... , a respectively , so that α1 , ... , α1 and a1 + ... CHARACTERISTIC EQUATION Estimates of characteristic roots.
Page 218
... characteristic roots of A are equal to 0 . = I. 22. Show that there exist no matrices A , B such that AB - BA 23. Show that the constant term in the minimum polynomial of A vanishes if and only if A is singular . 24. Show that the zeros ...
... characteristic roots of A are equal to 0 . = I. 22. Show that there exist no matrices A , B such that AB - BA 23. Show that the constant term in the minimum polynomial of A vanishes if and only if A is singular . 24. Show that the zeros ...
Page 323
... characteristic roots of A are , in modulus , less than or equal to 1. ' Prove this result by the use of triangular canonical forms . 10. Let 1 , ... , λn be the characteristic roots of A and μ1 , ... , μn the ( neces- sarily real ) ...
... characteristic roots of A are , in modulus , less than or equal to 1. ' Prove this result by the use of triangular canonical forms . 10. Let 1 , ... , λn be the characteristic roots of A and μ1 , ... , μn the ( neces- sarily real ) ...
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