An Introduction to Linear AlgebraClarendon Press, 1963 - 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 it ... deduce Theorem 2.5.2 ( p . 63 ) . Also deduce that , if { X1 , ... , Xn } 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 it ... deduce Theorem 2.5.2 ( p . 63 ) . Also deduce that , if { X1 , ... , Xn } is an orthonormal basis of V1 , then , for ...
Page 220
... Deduce that ( det A ) 2 - △ = ( − 1 ) In ( n − 1 ) † ƒ' ́ ( 0 , ) . T = 1 n ( −1 ) ( n − 1 ) ( n − 2 ) n " , where A denotes the matrix defined in the preceding question . 44. Show that the matrix A defined in No. 42 satisfies the ...
... Deduce that ( det A ) 2 - △ = ( − 1 ) In ( n − 1 ) † ƒ' ́ ( 0 , ) . T = 1 n ( −1 ) ( n − 1 ) ( n − 2 ) n " , where A denotes the matrix defined in the preceding question . 44. Show that the matrix A defined in No. 42 satisfies the ...
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
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