An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 44
... manifold ' , derived by abstraction from that of a vector space , and shall study the properties of this abstract system , returning from time to time to the particular ... linear manifold and 44 VECTOR SPACES AND LINEAR MANIFOLDS II , § 2.2.
... manifold ' , derived by abstraction from that of a vector space , and shall study the properties of this abstract system , returning from time to time to the particular ... linear manifold and 44 VECTOR SPACES AND LINEAR MANIFOLDS II , § 2.2.
Page 128
... linear mapping of one linear manifold onto another preserves linear dependence but not necessarily linear independence . Show further that if the dimensionalities of the two linear manifolds are equal , then linear independence is also ...
... linear mapping of one linear manifold onto another preserves linear dependence but not necessarily linear independence . Show further that if the dimensionalities of the two linear manifolds are equal , then linear independence is also ...
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