An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 39
... numbers is a field if , whenever we have a , b = F , we also have a + b , a - b , ab e F and , for b 0 , a / b € F. Obvious instances of fields are the set of all rational numbers , the set of all real numbers , and the set of all complex ...
... numbers is a field if , whenever we have a , b = F , we also have a + b , a - b , ab e F and , for b 0 , a / b € F. Obvious instances of fields are the set of all rational numbers , the set of all real numbers , and the set of all complex ...
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Leonid Mirsky. numbers ( the real field ) and the set of all complex numbers ( the complex field ) . 1 = It may be of interest to note that every field contains the field of rational numbers . For , since a field & contains a number ...
Leonid Mirsky. numbers ( the real field ) and the set of all complex numbers ( the complex field ) . 1 = It may be of interest to note that every field contains the field of rational numbers . For , since a field & contains a number ...
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... numbers , the real numbers , and the complex numbers , with 0 excluded in each case , form infinite abelian groups with respect to ordinary multiplication . In each case the unit element is 1 , and the inverse of a is 1 / a = a - 1 . It ...
... numbers , the real numbers , and the complex numbers , with 0 excluded in each case , form infinite abelian groups with respect to ordinary multiplication . In each case the unit element is 1 , and the inverse of a is 1 / a = a - 1 . It ...
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