An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 123
... linear transformations of projective space into itself . These ... transformation . An isomorphism between two linear manifolds M and M * is ... LINEAR OPERATORS AND THEIR REPRESENTATIONS 123 Isomorphisms and automorphisms of linear manifolds.
... linear transformations of projective space into itself . These ... transformation . An isomorphism between two linear manifolds M and M * is ... LINEAR OPERATORS AND THEIR REPRESENTATIONS 123 Isomorphisms and automorphisms of linear manifolds.
Page 128
... linear transformation of the class of integrable functions into itself . Operators such as ( 4.4.2 ) occur in the theory of integral equations . Many other ' integral transforms ' involve linear ... transformation of a linear manifold M into ...
... linear transformation of the class of integrable functions into itself . Operators such as ( 4.4.2 ) occur in the theory of integral equations . Many other ' integral transforms ' involve linear ... transformation of a linear manifold M into ...
Page 129
... linear transformation of the n - dimensional linear manifold M into itself ; M1 is the submanifold consisting of elements of the form L ( X ) ( X = M ) ; and M , is the submanifold of elements X = M such that L ( X ) = ~ , where is the ...
... linear transformation of the n - dimensional linear manifold M into itself ; M1 is the submanifold consisting of elements of the form L ( X ) ( X = M ) ; and M , is the submanifold of elements X = M such that L ( X ) = ~ , where is the ...
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