An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 61
... coordinate system in S. → If now the coordinates , with respect to C , of points X , YES are ( X1 , X2 , X3 ) , ( Y1 , Y2 , Y3 ) respectively , then the coordinates of points corresponding to the segments aox , ox + or are ( αX1 , αX2 ...
... coordinate system in S. → If now the coordinates , with respect to C , of points X , YES are ( X1 , X2 , X3 ) , ( Y1 , Y2 , Y3 ) respectively , then the coordinates of points corresponding to the segments aox , ox + or are ( αX1 , αX2 ...
Page 62
... coordinates be introduced in three - dimensional space , and let ( x1 , x2 , 3 ) , ( Y1 , Y2 , Y3 ) be the coordinates of two points . We may think of these triads as vectors x , y . The expression X1Y1 + X2Y2 + x3Y3 ( which is familiar ...
... coordinates be introduced in three - dimensional space , and let ( x1 , x2 , 3 ) , ( Y1 , Y2 , Y3 ) be the coordinates of two points . We may think of these triads as vectors x , y . The expression X1Y1 + X2Y2 + x3Y3 ( which is familiar ...
Page 364
... coordinates . Let A1 , A2 , A3 be the characteristic roots of the real symmetric 3 × 3 matrix A ( ars ) and let 51 ... coordinates and S ' the system for which 51 , 52 , 53 specify the directions of the axes , then , by Theorem 8.4.4 ( p ...
... coordinates . Let A1 , A2 , A3 be the characteristic roots of the real symmetric 3 × 3 matrix A ( ars ) and let 51 ... coordinates and S ' the system for which 51 , 52 , 53 specify the directions of the axes , then , by Theorem 8.4.4 ( p ...
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