An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 71
... expressed in the form X y + y ' , where y Є U , y ' € U ' . = n n 18. Let U , V be two subspaces of V1 and let V ′ be a complement of V. Show that , if VCU and the only vector common to U and V ' is 0 , then u = V. n 19. Let U , V be ...
... expressed in the form X y + y ' , where y Є U , y ' € U ' . = n n 18. Let U , V be two subspaces of V1 and let V ′ be a complement of V. Show that , if VCU and the only vector common to U and V ' is 0 , then u = V. n 19. Let U , V be ...
Page 193
... expressed as the sum of r matrices of rank 1 . 10. By using the technique of E - operations prove that ( i ) a system of n homogeneous linear equations in n unknowns possesses a non - trivial solution if and only if the matrix of ...
... expressed as the sum of r matrices of rank 1 . 10. By using the technique of E - operations prove that ( i ) a system of n homogeneous linear equations in n unknowns possesses a non - trivial solution if and only if the matrix of ...
Page 259
... expressed as a product of transpositions , the number of factors in the product is either always even or always odd . † It is natural , therefore , to call a permutation even or odd according as it is the product of an even or an odd ...
... expressed as a product of transpositions , the number of factors in the product is either always even or always odd . † It is natural , therefore , to call a permutation even or odd according as it is the product of an even or an odd ...
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