An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
À l'intérieur du livre
Résultats 1-3 sur 9
Page 233
... rotation ' will be taken to mean a rotation of the plane about the origin . As usual , a rotation will be reckoned ... ROTATIONS IN THE PLANE Rotations in the plane.
... rotation ' will be taken to mean a rotation of the plane about the origin . As usual , a rotation will be reckoned ... ROTATIONS IN THE PLANE Rotations in the plane.
Page 245
... rotation , but the skew - symmetric matrix of the product of two rotations is also easy to evaluate . THEOREM 8.4.10 . Let R be the product of the two rotations R1 , R2 , carried out in that order , and suppose that none of the three ...
... rotation , but the skew - symmetric matrix of the product of two rotations is also easy to evaluate . THEOREM 8.4.10 . Let R be the product of the two rotations R1 , R2 , carried out in that order , and suppose that none of the three ...
Page 268
... rotation R ( a ) through an angle a . The group of space rotations about the origin is represented by the rotation group of 3x3 matrices . The intimate connexion between matrices and linear transforma- tions of linear manifolds has ...
... rotation R ( a ) through an angle a . The group of space rotations about the origin is represented by the rotation group of 3x3 matrices . The intimate connexion between matrices and linear transforma- tions of linear manifolds has ...
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