An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Leonid Mirsky. A hermitian form of type a11x 1 + ... + αn xnxn is called diagonal . Here the coefficients a , ... , a , are necessarily real since they are the diagonal elements of a hermitian matrix . The form 11 + ... + xnxn is known ...
Leonid Mirsky. A hermitian form of type a11x 1 + ... + αn xnxn is called diagonal . Here the coefficients a , ... , a , are necessarily real since they are the diagonal elements of a hermitian matrix . The form 11 + ... + xnxn is known ...
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Leonid Mirsky. THEOREM 12.6.3 . ( Equivalence theorem for hermitian forms ) Two hermitian forms are equivalent with respect to the group of complex non - singular linear transformations if and only if they have the same rank and the same ...
Leonid Mirsky. THEOREM 12.6.3 . ( Equivalence theorem for hermitian forms ) Two hermitian forms are equivalent with respect to the group of complex non - singular linear transformations if and only if they have the same rank and the same ...
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Leonid Mirsky. XIII DEFINITE AND INDEFINITE FORMS In the previous chapter quadratic and hermitian forms were ... form in the variables x1 , ... , xn . ( i ) is POSITIVE DEFINITE ( NEGATIVE DEFINITE ) if ☀ > 0 ( $ < 0 ) except when x1 ...
Leonid Mirsky. XIII DEFINITE AND INDEFINITE FORMS In the previous chapter quadratic and hermitian forms were ... form in the variables x1 , ... , xn . ( i ) is POSITIVE DEFINITE ( NEGATIVE DEFINITE ) if ☀ > 0 ( $ < 0 ) except when x1 ...
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