An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 35
Page 186
... equivalence between matrices is reflexive , symmetric , and transitive . These three properties occur so persistently in different mathematical situations that it is useful to introduce an abstract concept of equivalence , of which ...
... equivalence between matrices is reflexive , symmetric , and transitive . These three properties occur so persistently in different mathematical situations that it is useful to introduce an abstract concept of equivalence , of which ...
Page 187
... equivalence relation has been defined . Then S can be subdivided into classes of elements in such a way that ( i ) each element belongs to precisely one class , ( ii ) two ... equivalence VI , § 6.5 THE GENERAL CONCEPT OF EQUIVALENCE 187.
... equivalence relation has been defined . Then S can be subdivided into classes of elements in such a way that ( i ) each element belongs to precisely one class , ( ii ) two ... equivalence VI , § 6.5 THE GENERAL CONCEPT OF EQUIVALENCE 187.
Page 189
... equivalence with respect to a set of operators , an equivalence class simply consists of all elements which can be transformed into a specified element by means of suitably chosen operators . Several examples of equivalence with respect ...
... equivalence with respect to a set of operators , an equivalence class simply consists of all elements which can be transformed into a specified element by means of suitably chosen operators . Several examples of equivalence with respect ...
Table des matières
DETERMINANTS VECTORS MATRICES | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
12 autres sections non affichées
Autres éditions - Tout afficher
Expressions et termes fréquents
A₁ algebra assertion automorphism B₁ basis bilinear form bilinear operator C₁ canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix 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 values vector space view of Theorem write x₁ xTAx y₁ zero α₁