An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 25
... result . If , however , D = 0 this obvious device fails , and we have recourse to Theorem 1.5.1 . Let us regard D as ... result . † . Our next result - the main result of the present section - was discovered by Jacobi in 1833 . THEOREM ...
... result . If , however , D = 0 this obvious device fails , and we have recourse to Theorem 1.5.1 . Let us regard D as ... result . † . Our next result - the main result of the present section - was discovered by Jacobi in 1833 . THEOREM ...
Page 156
... result . 5.5.5 . An interesting application of matrix technique can be made in the calculus of observations . Consider the system of linear equations a11 x1 + ... + a1n xn = b1 am1 x1 + ... + amn xn = bm ( 5.5.4 ) in which m > n , and ...
... result . 5.5.5 . An interesting application of matrix technique can be made in the calculus of observations . Consider the system of linear equations a11 x1 + ... + a1n xn = b1 am1 x1 + ... + amn xn = bm ( 5.5.4 ) in which m > n , and ...
Page 205
... result by determining an annihilating polynomial of degree n . It will be necessary to consider polynomials in a scalar variable à which have matrix coefficients , and we shall always write each power of λ to the right of the ...
... result by determining an annihilating polynomial of degree n . It will be necessary to consider polynomials in a scalar variable à which have matrix coefficients , and we shall always write each power of λ to the right of 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