An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 70
... deduce Theorem 2.3.5 ( p . 54 ) . ✓ 7. Show that a subset N of a linear manifold M is a submanifold if and only if ... deduce Theorem 2.5.2 ( p . 63 ) . n Also deduce that , if { X1 , ... , X } is an orthonormal basis of V1 , then , for ...
... deduce Theorem 2.3.5 ( p . 54 ) . ✓ 7. Show that a subset N of a linear manifold M is a submanifold if and only if ... deduce Theorem 2.5.2 ( p . 63 ) . n Also deduce that , if { X1 , ... , X } is an orthonormal basis of V1 , then , for ...
Page 324
... Deduce that | ƒ ( A , B ) | 2 < ƒ ( A , A ) .ƒ ( B , B ) . N ( A + B ) < N ( A ) + N ( B ) , where N ( A ) = { ƒ ( A , A ) } } . 21. Deduce from the inequality ( 10.4.4 ) , p . 309 , that all characteristic roots of a hermitian matrix ...
... Deduce that | ƒ ( A , B ) | 2 < ƒ ( A , A ) .ƒ ( B , B ) . N ( A + B ) < N ( A ) + N ( B ) , where N ( A ) = { ƒ ( A , A ) } } . 21. Deduce from the inequality ( 10.4.4 ) , p . 309 , that all characteristic roots of a hermitian matrix ...
Page 325
... deduce that A possesses n linearly independent characteristic vectors . Hence show that a matrix , whose minimum polynomial is the pro- duct of distinct linear factors , is similar to a diagonal matrix . = 35. Let w1 , ... , we be the ...
... deduce that A possesses n linearly independent characteristic vectors . Hence show that a matrix , whose minimum polynomial is the pro- duct of distinct linear factors , is similar to a diagonal matrix . = 35. Let w1 , ... , we be the ...
Table des matières
DETERMINANTS VECTORS MATRICES | 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 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