An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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Page 76
... TRIANGULAR MATRIX is one that is either upper triangular or lower triangular . If a matrix is both upper triangular and lower triangular , it is clearly diagonal . DEFINITION 3.2.7 . The TRANSPOSE AT of a matrix A is the matrix obtained ...
... TRIANGULAR MATRIX is one that is either upper triangular or lower triangular . If a matrix is both upper triangular and lower triangular , it is clearly diagonal . DEFINITION 3.2.7 . The TRANSPOSE AT of a matrix A is the matrix obtained ...
Page 307
... triangular matrix . This statement is equally valid whether the term ' triangular ' is taken to mean ' upper triangular ' or ' lower triangular ' . We shall prove it in the first instance for the former interpretation and then deduce at ...
... triangular matrix . This statement is equally valid whether the term ' triangular ' is taken to mean ' upper triangular ' or ' lower triangular ' . We shall prove it in the first instance for the former interpretation and then deduce at ...
Page 316
... triangular matrix of order m . Writing Q = dg ( Q1 , ... , Qk ) , we obtain S - 1AS = Q - 1P - 1APQ = = S = PQ , dg ... ( triangular ) matrices if there exists a matrix S such that S - AS , S - 1BS , S - 1CS , ... are all diagonal ...
... triangular matrix of order m . Writing Q = dg ( Q1 , ... , Qk ) , we obtain S - 1AS = Q - 1P - 1APQ = = S = PQ , dg ... ( triangular ) matrices if there exists a matrix S such that S - AS , S - 1BS , S - 1CS , ... are all diagonal ...
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