An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 126
... Further instances of linear operators The idea of a linear operator introduced in Definition 4.2.2 pervades , in one form or another , a large part of mathematics . The operators we have encountered so far have all been associated with ...
... Further instances of linear operators The idea of a linear operator introduced in Definition 4.2.2 pervades , in one form or another , a large part of mathematics . The operators we have encountered so far have all been associated with ...
Page 195
... further development of the subject at a somewhat less elemen- tary level , and enables us to deal with a series of problems which are beyond the range of the methods employed previously . The idea of the characteristic equation will be ...
... further development of the subject at a somewhat less elemen- tary level , and enables us to deal with a series of problems which are beyond the range of the methods employed previously . The idea of the characteristic equation will be ...
Page 385
... further the group of transformations , we are led to refinements of the previous systems of classification . By far the most important system that arises in this way is that of ' metric classification ' . Let ( 12.5.1 ) again be the ...
... further the group of transformations , we are led to refinements of the previous systems of classification . By far the most important system that arises in this way is that of ' metric classification ' . Let ( 12.5.1 ) again be 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