An Introduction to Linear AlgebraClarendon Press, 1972 - 440 pages |
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Page 183
... SYMMETRIC if aij ( i , j = 1 , ... , n ) , i.e. if AT A. † = aji = The symmetry mentioned in the definition is , of course , symmetry with respect to the diagonal . EXERCISE 6.4.2 . If A is a rectangular matrix , show that ATA is a ...
... SYMMETRIC if aij ( i , j = 1 , ... , n ) , i.e. if AT A. † = aji = The symmetry mentioned in the definition is , of course , symmetry with respect to the diagonal . EXERCISE 6.4.2 . If A is a rectangular matrix , show that ATA is a ...
Page 244
... symmetric matrices . The matrix S asso- ciated with the rotation R will be called the skew - symmetric matrix of R. Similarly , the ( proper ) orthogonal matrix A which represents R in the sense that R is specified by the equation x ...
... symmetric matrices . The matrix S asso- ciated with the rotation R will be called the skew - symmetric matrix of R. Similarly , the ( proper ) orthogonal matrix A which represents R in the sense that R is specified by the equation x ...
Page 301
... symmetric ) matrix with distinct characteristic roots is unitarily ( orthogonally ) similar to a diagonal matrix . n Let λ ............ .λ be the ( distinct ) characteristic roots of a hermitian or real symmetric matrix A , and denote ...
... symmetric ) matrix with distinct characteristic roots is unitarily ( orthogonally ) similar to a diagonal matrix . n Let λ ............ .λ be the ( distinct ) characteristic roots of a hermitian or real symmetric matrix A , and denote ...
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