An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 205
... course , a polynomial such that f ( B ) / g ( B ) = √ ( B ) . The possibility of expressing every rational function of a matrix as a polynomial marks a vital point of difference between matrix algebra and the algebra of numbers . 7.4.2 ...
... course , a polynomial such that f ( B ) / g ( B ) = √ ( B ) . The possibility of expressing every rational function of a matrix as a polynomial marks a vital point of difference between matrix algebra and the algebra of numbers . 7.4.2 ...
Page 252
... course , important to bear in mind that ab is , in general , distinct from ba . DEFINITION 9.1.1 . Let G be a set of elements a , b , c , ... , and let R be a rule of composition ( called multiplication ) , defined for all ordered pairs ...
... course , important to bear in mind that ab is , in general , distinct from ba . DEFINITION 9.1.1 . Let G be a set of elements a , b , c , ... , and let R be a rule of composition ( called multiplication ) , defined for all ordered pairs ...
Page 395
... course , to a certain value class , but there is fortunately no possibility of confusion since the two forms belong , in fact , to the same value class . THEOREM 13.1.1 . If A is a real symmetric matrix , then the her- mitian form = 4 ...
... course , to a certain value class , but there is fortunately no possibility of confusion since the two forms belong , in fact , to the same value class . THEOREM 13.1.1 . If A is a real symmetric matrix , then the her- mitian form = 4 ...
Table des matières
PART | 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 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