An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 360
... quadratic form & is the rank of the matrix of p . ( ii ) The rank of a quadratic operator is the rank of any quadratic form representing that operator . In view of Theorem 12.1.5 , the second part of this definition is unambiguous ...
... quadratic form & is the rank of the matrix of p . ( ii ) The rank of a quadratic operator is the rank of any quadratic form representing that operator . In view of Theorem 12.1.5 , the second part of this definition is unambiguous ...
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 ...
Page 391
... quadratic form Q ( x1 , ... , xn ) , and let à be a characteristic root of A. Show that there exist values of x1 , ... , xn , not all zero , which satisfy the equation Q ( x1 , ... , xn ) = λ ( x2 + ... + x2 ) . · 9. An n - ary quadratic ...
... quadratic form Q ( x1 , ... , xn ) , and let à be a characteristic root of A. Show that there exist values of x1 , ... , xn , not all zero , which satisfy the equation Q ( x1 , ... , xn ) = λ ( x2 + ... + x2 ) . · 9. An n - ary quadratic ...
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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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