An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 127
... operator зги аги зи ; + : + = K მე მყ ' Oz2 ди · at 22 axat 22 22 + Əy2 Əza a K Ət ' ( 4.4.1 ) - then this equation can be rewritten in the operational form Qu 0. Now the functions of the four variables x , y , z , t which possess ...
... operator зги аги зи ; + : + = K მე მყ ' Oz2 ди · at 22 axat 22 22 + Əy2 Əza a K Ət ' ( 4.4.1 ) - then this equation can be rewritten in the operational form Qu 0. Now the functions of the four variables x , y , z , t which possess ...
Page 358
... operator with respect to suitable bases in M if and only if they are congruent , i.e. B = PTAP , where P is non - singular . Suppose that the matrices A and B represent the same quadratic operator ( X , X ) with respect to bases B and B ...
... operator with respect to suitable bases in M if and only if they are congruent , i.e. B = PTAP , where P is non - singular . Suppose that the matrices A and B represent the same quadratic operator ( X , X ) with respect to bases B and B ...
Page 361
... operators . X ) Let M be a linear manifold of dimensionality n and let ø ( X , be a quadratic operator on M. If ( X , Y ) is a bilinear operator which gives rise to the quadratic operator ( X , X ) when the substitution Y = X is made ...
... operators . X ) Let M be a linear manifold of dimensionality n and let ø ( X , be a quadratic operator on M. If ( X , Y ) is a bilinear operator which gives rise to the quadratic operator ( X , X ) when the substitution Y = X is made ...
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