An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 63
Page 203
... polynomial annihilating A is proved once again . Among all non - zero polynomials annihilating A we now consider those of least degree , and by multiplying them by suitable ... polynomial of a matrix is VII , § 7.4 203 THE MINIMUM POLYNOMIAL.
... polynomial annihilating A is proved once again . Among all non - zero polynomials annihilating A we now consider those of least degree , and by multiplying them by suitable ... polynomial of a matrix is VII , § 7.4 203 THE MINIMUM POLYNOMIAL.
Page 204
... polynomial which annihilates the matrix . Denote the minimum polynomial of A by μ ( λ ) , and let ƒ ( ^ ) be a polynomial such that ƒ ( A ) = O. By the division algorithm , there exist polynomials q ( λ ) , r ( ^ ) such that ƒ ( λ ) = q ...
... polynomial which annihilates the matrix . Denote the minimum polynomial of A by μ ( λ ) , and let ƒ ( ^ ) be a polynomial such that ƒ ( A ) = O. By the division algorithm , there exist polynomials q ( λ ) , r ( ^ ) such that ƒ ( λ ) = q ...
Page 207
... polynomial of A is A - 1 0 - -2 0 0 λ + 1 -1 = λ3 - 2λ + 1 . - -1 λ - - Now , long division of 2 ) 3 — 3λ5 + λa + λ2 ... polynomial form . This is achieved by carrying out the process explained in the proof of Theorem 7.4.3 but using the ...
... polynomial of A is A - 1 0 - -2 0 0 λ + 1 -1 = λ3 - 2λ + 1 . - -1 λ - - Now , long division of 2 ) 3 — 3λ5 + λa + λ2 ... polynomial form . This is achieved by carrying out the process explained in the proof of Theorem 7.4.3 but using the ...
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
12 autres sections non affichées
Autres éditions - Tout afficher
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