An Introduction to Linear AlgebraClarendon Press, 1955 - 433 pages |
À l'intérieur du livre
Résultats 1-3 sur 80
Page 59
... implies linear dependence of X1 , ... , X. The proof of the assertion is therefore complete . As an immediate ... implies R , and Q implies S. DEFINITION 2.4.2 . If B = { E1 , ... II , § 2.4 VECTOR REPRESENTATION OF MANIFOLDS 59.
... implies linear dependence of X1 , ... , X. The proof of the assertion is therefore complete . As an immediate ... implies R , and Q implies S. DEFINITION 2.4.2 . If B = { E1 , ... II , § 2.4 VECTOR REPRESENTATION OF MANIFOLDS 59.
Page 98
... implies f ( A ) + g ( A ) = f ( A ) , ( 3.7.2 ) f ( x ) g ( x ) = p ( x ) implies f ( A ) g ( A ) = $ ( A ) . ( 3.7.3 ) The proof of ( 3.7.2 ) is trivial and we leave it to the reader . To establish ( 3.7.3 ) we write * 8 f ( x ) = £ a ...
... implies f ( A ) + g ( A ) = f ( A ) , ( 3.7.2 ) f ( x ) g ( x ) = p ( x ) implies f ( A ) g ( A ) = $ ( A ) . ( 3.7.3 ) The proof of ( 3.7.2 ) is trivial and we leave it to the reader . To establish ( 3.7.3 ) we write * 8 f ( x ) = £ a ...
Page 286
... implies ( ii ) . - n⋅ Next , let ( ii ) be given , i.e d ( LVn ) = d ( L2Vn ) . LVR = n L2 and therefore , by Theorem 9.5.1 , G ( L ) Thus ( ii ) implies ( iii ) . = = Then LVn ' Finally , let ( iii ) be given and write U LVn . Then ...
... implies ( ii ) . - n⋅ Next , let ( ii ) be given , i.e d ( LVn ) = d ( L2Vn ) . LVR = n L2 and therefore , by Theorem 9.5.1 , G ( L ) Thus ( ii ) implies ( iii ) . = = Then LVn ' Finally , let ( iii ) be given and write U LVn . Then ...
Table des matières
PART | 3 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
11 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 dimensionality E-operations equal equivalence EXERCISE exists follows functions given Hence hermitian form hermitian matrix identity implies inequality integers isomorphic linear combination 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 nxn matrix obtain orthogonal matrix positive definite possesses proof of Theorem prove quadratic form quadric rank reduces 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 w₁ write x₁ y₁ zero α₁