An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 71
Page 62
... complex vectors . We shall , therefore , introduce modified definitions of inner product and length for the general case of complex vectors ; these definitions will naturally reduce to ( 2.5.1 ) and ( 2.5.2 ) when the vectors are real ...
... complex vectors . We shall , therefore , introduce modified definitions of inner product and length for the general case of complex vectors ; these definitions will naturally reduce to ( 2.5.1 ) and ( 2.5.2 ) when the vectors are real ...
Page 264
... complex numbers , and that the correspondence is once again given by the scheme ( 9.2.2 ) . The analogy , exhibited by the two isomorphisms , between the algebra of complex numbers and that of matrices of type ( 9.2.1 ) , makes it ...
... complex numbers , and that the correspondence is once again given by the scheme ( 9.2.2 ) . The analogy , exhibited by the two isomorphisms , between the algebra of complex numbers and that of matrices of type ( 9.2.1 ) , makes it ...
Page 396
... complex ( real ) non- singular linear transformation . If S ( 4 ) , ( 4 ) denote the sets of values assumed by 4 , respectively as their variables take all complex ( real ) values , not all zero , then S ( 4 ) 6 ( 4 ) . = We shall state ...
... complex ( real ) non- singular linear transformation . If S ( 4 ) , ( 4 ) denote the sets of values assumed by 4 , respectively as their variables take all complex ( real ) values , not all zero , then S ( 4 ) 6 ( 4 ) . = We shall state ...
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