An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 62
... complex vectors . We shall , therefore , introduce modified definitions of inner product and length for the general case of complex vectors ; these definitions will naturally reduce to ( 2.5.1 ) and ( 2.5.2 ) when the vectors are real ...
... complex vectors . We shall , therefore , introduce modified definitions of inner product and length for the general case of complex vectors ; these definitions will naturally reduce to ( 2.5.1 ) and ( 2.5.2 ) when the vectors are real ...
Page 376
... complex ( real ) non - singular linear transforma- tion , then is said to be EQUIVALENT to under the group of complex ( real ) non - singular linear transformations . The two groups of transformations mentioned here will be denoted ...
... complex ( real ) non - singular linear transforma- tion , then is said to be EQUIVALENT to under the group of complex ( real ) non - singular linear transformations . The two groups of transformations mentioned here will be denoted ...
Page 381
... Complex affine classification Pair of distinct planes Repeated plane Suppose that ( 12.5.1 ) is again the equation ... complex affine collinea- tion is a complex non - singular linear transformation of coordinates which transforms the ...
... Complex affine classification Pair of distinct planes Repeated plane Suppose that ( 12.5.1 ) is again the equation ... complex affine collinea- tion is a complex non - singular linear transformation of coordinates which transforms 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