An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 362
... quadratic operator ( X , X ) is represented by the quadratic form x " Ax , its polarized operator ( X , Y ) is represented , with respect to the same ... QUADRATIC , AND HERMITIAN FORMS XII , § 12.1 Orthogonal reduction to diagonal form.
... quadratic operator ( X , X ) is represented by the quadratic form x " Ax , its polarized operator ( X , Y ) is represented , with respect to the same ... QUADRATIC , AND HERMITIAN FORMS XII , § 12.1 Orthogonal reduction to diagonal form.
Page 370
... quadratic form of rank r to diagonal form in which the number of non - vanishing 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 ...
... quadratic form of rank r to diagonal form in which the number of non - vanishing 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 ...
Page 376
... quadratic form 4 but the entire class of quadratic forms that can be obtained from 4 by non - singular linear transformations . All these quadratic forms will represent , when equated to 0 , the same conic C , referred in each case to a ...
... quadratic form 4 but the entire class of quadratic forms that can be obtained from 4 by non - singular linear transformations . All these quadratic forms will represent , when equated to 0 , the same conic C , referred in each case to a ...
Table des matières
DETERMINANTS VECTORS MATRICES | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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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