An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 58
... corresponds to Z in M. It is instructive to express the same idea in yet another way by making use of the functional ... corresponding elements in M ' , then the resulting elements in M and M ' again correspond to each other . Some ...
... corresponds to Z in M. It is instructive to express the same idea in yet another way by making use of the functional ... corresponding elements in M ' , then the resulting elements in M and M ' again correspond to each other . Some ...
Page 59
... corresponding to each XEM , there exist unique scalars x1 , ... , x , such that X = x1 E1 + ... + x , Er . A ... corresponds to ax . Again , if Ye M corresponds to ye V ,, then X + Y corresponds to x + y . This proves the theorem . † The ...
... corresponding to each XEM , there exist unique scalars x1 , ... , x , such that X = x1 E1 + ... + x , Er . A ... corresponds to ax . Again , if Ye M corresponds to ye V ,, then X + Y corresponds to x + y . This proves the theorem . † The ...
Page 80
... corresponding ideas for vectors . In introducing next the idea of matrix multiplication , however , we break fresh ground . DEFINITION 3.3.3 . Suppose that A is an 1 × m matrix and B an mxn matrix , so that the number of columns of A is ...
... corresponding ideas for vectors . In introducing next the idea of matrix multiplication , however , we break fresh ground . DEFINITION 3.3.3 . Suppose that A is an 1 × m matrix and B an mxn matrix , so that the number of columns of A is ...
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