An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 353
... bilinear and quadratic types 12.1.1 . It is necessary at this stage to make use of some of the properties of linear ... BILINEAR OPERATOR on M and N. EXERCISE 12.1.1 . Show that the relation p ( aX + a'X ' , BY + ẞ'Y ' ) = aßp ( X , Y ) ...
... bilinear and quadratic types 12.1.1 . It is necessary at this stage to make use of some of the properties of linear ... BILINEAR OPERATOR on M and N. EXERCISE 12.1.1 . Show that the relation p ( aX + a'X ' , BY + ẞ'Y ' ) = aßp ( X , Y ) ...
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... bilinear operator on M and n , and if = R ( Y ; C ) , x = R ( X ; B ) , y ¢ ( X , Y ) = x ^ Ay , ( as ) is defined ... bilinear operators . DEFINITION 12.1.2 . Any polynomial m n Z α , x , y1 = x2Ay , Σars Ys r = 18 = 1 ( 12.1.3 ) where ...
... bilinear operator on M and n , and if = R ( Y ; C ) , x = R ( X ; B ) , y ¢ ( X , Y ) = x ^ Ay , ( as ) is defined ... bilinear operators . DEFINITION 12.1.2 . Any polynomial m n Z α , x , y1 = x2Ay , Σars Ys r = 18 = 1 ( 12.1.3 ) where ...
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... bilinear operator which it represents with respect to B , C is uniquely determined by ( 12.1.2 ) and ( 12.1.1 ) . The representation of a bilinear operator by a bilinear form ( or by a matrix ) depends , of course , on the arbitrary ...
... bilinear operator which it represents with respect to B , C is uniquely determined by ( 12.1.2 ) and ( 12.1.1 ) . The representation of a bilinear operator by a bilinear form ( or by a matrix ) depends , of course , on the arbitrary ...
Table des matières
DETERMINANTS VECTORS MATRICES | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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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