An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 48
Page 142
... coefficients . Then whose coefficients are involved in △ form ; ( i ) the r equations of a system S'equivalent to ( ii ) if arbitrary values are assigned to the n - r ' disposable ' unknowns in S ' , whose coefficients are not elements ...
... coefficients . Then whose coefficients are involved in △ form ; ( i ) the r equations of a system S'equivalent to ( ii ) if arbitrary values are assigned to the n - r ' disposable ' unknowns in S ' , whose coefficients are not elements ...
Page 205
... coefficients of depend on A as well as on ƒ and g . On the other hand , there exists , of course , a polynomial ... coefficients , and we shall always write each power of λ to the right of the corresponding matrix coefficient . Let f ( λ ) ...
... coefficients of depend on A as well as on ƒ and g . On the other hand , there exists , of course , a polynomial ... coefficients , and we shall always write each power of λ to the right of the corresponding matrix coefficient . Let f ( λ ) ...
Page 370
... coefficients is not equal to r . It is , however , almost obvious that such a reduction is not possible . THEOREM 12.3.4 . If a quadratic form of rank r is reduced by a non - singular linear transformation to diagonal form , then the ...
... coefficients is not equal to r . It is , however , almost obvious that such a reduction is not possible . THEOREM 12.3.4 . If a quadratic form of rank r is reduced by a non - singular linear transformation to diagonal form , then the ...
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