An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 6
... consisting of the single element a11 is , of course , equal to a11 . Further , we have = € ( 1 , 2 ) α11a22 + € ( 2 , 1 ) α12 a21 = a11a22 - α1221 ; ε ( 1 , 2 , 3 ) α11 α22 α33 + e ( 1 , 3 , 2 ) α11 A23 A32 + a11 a12 a21 a22 = a11 12 13 ...
... consisting of the single element a11 is , of course , equal to a11 . Further , we have = € ( 1 , 2 ) α11a22 + € ( 2 , 1 ) α12 a21 = a11a22 - α1221 ; ε ( 1 , 2 , 3 ) α11 α22 α33 + e ( 1 , 3 , 2 ) α11 A23 A32 + a11 a12 a21 a22 = a11 12 13 ...
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... consisting of all functions continuous in the interval 0 < x < 1 - possess arbitrarily large sets of linearly independent elements . However , our main concern is with those linear manifolds for which that is not the case . DEFINITION ...
... consisting of all functions continuous in the interval 0 < x < 1 - possess arbitrarily large sets of linearly independent elements . However , our main concern is with those linear manifolds for which that is not the case . DEFINITION ...
Page 129
... consisting of the vectors ( 1 , i ) , ( 1 , −i ) . 9. L is a linear transformation of V , into itself , B is a basis of Vn , and B ' is another basis obtained from B by rearrangement of the vectors in B. Determine the relation between ...
... consisting of the vectors ( 1 , i ) , ( 1 , −i ) . 9. L is a linear transformation of V , into itself , B is a basis of Vn , and B ' is another basis obtained from B by rearrangement of the vectors in B. Determine the relation between ...
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