An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 219
... satisfies the equation A2 = I is similar to the matrix dg ( i , —i ) . -- 35. Show that , if A is a non - singular nxn matrix , then the coefficient of À in the characteristic polynomial x ( λ ) of A is equal to ( − 1 ) ” - 1 | A | tr ...
... satisfies the equation A2 = I is similar to the matrix dg ( i , —i ) . -- 35. Show that , if A is a non - singular nxn matrix , then the coefficient of À in the characteristic polynomial x ( λ ) of A is equal to ( − 1 ) ” - 1 | A | tr ...
Page 299
... satisfies ( 10.2.7 ) . Each μ , in the above proof can , in general , be chosen in k distinct ways , where k is the degree of f . Hence our construction yields , in general , k2 solutions of ( 10.2.7 ) . This reasoning shows , in ...
... satisfies ( 10.2.7 ) . Each μ , in the above proof can , in general , be chosen in k distinct ways , where k is the degree of f . Hence our construction yields , in general , k2 solutions of ( 10.2.7 ) . This reasoning shows , in ...
Page 407
... satisfies at least one of the following two conditions . ( i ) A possesses a negative principal minor of even order ... satisfies either of the two stated conditions , then it is indefinite . It remains , therefore , to show that if A is ...
... satisfies at least one of the following two conditions . ( i ) A possesses a negative principal minor of even order ... satisfies either of the two stated conditions , then it is indefinite . It remains , therefore , to show that if A is ...
Table des matières
PART | 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 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