An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 75
... equal if and only if their corresponding elements are equal . In future we shall not , as a rule , mention the reference field F explicitly but shall assume tacitly that such a field has been given . If F is the real ( complex ) field ...
... equal if and only if their corresponding elements are equal . In future we shall not , as a rule , mention the reference field F explicitly but shall assume tacitly that such a field has been given . If F is the real ( complex ) field ...
Page 204
... equal to a polynomial in A whose coefficients depend on f , g and A. It is sufficient to show that { g ( A ) } - 1 is equal to a polynomial in A. We write S g ( A ) and denote by = μ ( λ ) = λk + α1 λk − 1 + ... + α - 1λ + α the ...
... equal to a polynomial in A whose coefficients depend on f , g and A. It is sufficient to show that { g ( A ) } - 1 is equal to a polynomial in A. We write S g ( A ) and denote by = μ ( λ ) = λk + α1 λk − 1 + ... + α - 1λ + α the ...
Page 341
... equal to 1 and all of whose remaining elements are equal to 0. Writing = Yrsm ( r , s = 1 , ... , n ; m > 1 ) ( Tm ) rs n we have I'm = Σ Yrsm I ( r , s ) ( m > 1 ) . ( 11.3.2 ) 7,8 = 1 The existence of lim T means that m - ∞ m lim ...
... equal to 1 and all of whose remaining elements are equal to 0. Writing = Yrsm ( r , s = 1 , ... , n ; m > 1 ) ( Tm ) rs n we have I'm = Σ Yrsm I ( r , s ) ( m > 1 ) . ( 11.3.2 ) 7,8 = 1 The existence of lim T means that m - ∞ m lim ...
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