An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 187
... classes of elements in such a way that ( i ) each element belongs to precisely one class , ( ii ) two elements belong to the same class if and only if they are equivalent . The proof is almost obvious . If x is any element of S , let C ...
... classes of elements in such a way that ( i ) each element belongs to precisely one class , ( ii ) two elements belong to the same class if and only if they are equivalent . The proof is almost obvious . If x is any element of S , let C ...
Page 255
... classes as the rule of composition . A residue class ( mod m ) is said to be prime to m if some number ( and therefore every number ) in it is prime to m . It is easy to show that the residue classes ( mod m ) prime to m form an abelian ...
... classes as the rule of composition . A residue class ( mod m ) is said to be prime to m if some number ( and therefore every number ) in it is prime to m . It is easy to show that the residue classes ( mod m ) prime to m form an abelian ...
Page 394
... class will now consist of one or more of the former classes ) it is , for some purposes , of even greater importance . 13.1 . The value classes 13.1.1 . DEFINITION 13.1.1 . Let & be a hermitian or a quadratic form in the variables x1 ...
... class will now consist of one or more of the former classes ) it is , for some purposes , of even greater importance . 13.1 . The value classes 13.1.1 . DEFINITION 13.1.1 . Let & be a hermitian or a quadratic form in the variables x1 ...
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