An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 53
Page 28
... assertion is seen to hold . If , on the other hand , the numbers a11 , ... , anı do not all vanish we may assume , without loss of generality , that a110 . In that case we subtract , for 2 , ... , n , ai / a11 times the first row from ...
... assertion is seen to hold . If , on the other hand , the numbers a11 , ... , anı do not all vanish we may assume , without loss of generality , that a110 . In that case we subtract , for 2 , ... , n , ai / a11 times the first row from ...
Page 66
... assertion since the first then follows as a trivial consequence . Write d ( V ) = r ( 1 ) and let X1 , ... , x be an orthonormal set of vectors in 2 , where 1 < k < r . By Corollary 1 to Theorem 2.5.4 and the corollary to Theorem 2.3.5 ...
... assertion since the first then follows as a trivial consequence . Write d ( V ) = r ( 1 ) and let X1 , ... , x be an orthonormal set of vectors in 2 , where 1 < k < r . By Corollary 1 to Theorem 2.5.4 and the corollary to Theorem 2.3.5 ...
Page 171
... assertion is obvious by Theorem 6.1.1 since an E - matrix is derived by an E - operation from a non - singular matrix . To prove the second assertion let E denote a given E - matrix , say of order n . Then I can be derived from E by a ...
... assertion is obvious by Theorem 6.1.1 since an E - matrix is derived by an E - operation from a non - singular matrix . To prove the second assertion let E denote a given E - matrix , say of order n . Then I can be derived from E by a ...
Table des matières
PART | 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 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