An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 156
... values of α1 , ... , a ,, not all zero , satisfying these equations . Since Xx + 10 , it may be normalized ; and it ... values ) have been determined as the result of experiments and that , owing to errors of observation , the system ...
... values of α1 , ... , a ,, not all zero , satisfying these equations . Since Xx + 10 , it may be normalized ; and it ... values ) have been determined as the result of experiments and that , owing to errors of observation , the system ...
Page 394
... values that the forms in question are capable of assuming . † Though this new classifica- tion is cruder than the ... values of x1 , ... , xn and = 0 for some values of X1 , ... , Xn , not all zero . A form which is positive semi ...
... values that the forms in question are capable of assuming . † Though this new classifica- tion is cruder than the ... values of x1 , ... , xn and = 0 for some values of X1 , ... , Xn , not all zero . A form which is positive semi ...
Page 396
... values assumed by 4 , respectively as their variables take all complex ( real ) values , not all zero , then S ( 4 ) 6 ( 4 ) . = We shall state the proof in the language of hermitian forms . Let = XTBX . = ф = XTAX ,屮 By hypothesis ...
... values assumed by 4 , respectively as their variables take all complex ( real ) values , not all zero , then S ( 4 ) 6 ( 4 ) . = We shall state the proof in the language of hermitian forms . Let = XTBX . = ф = XTAX ,屮 By hypothesis ...
Table des matières
DETERMINANTS VECTORS MATRICES | 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 C₁ canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix 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 values vector space view of Theorem write x₁ xTAx y₁ zero α₁