An Introduction to Linear AlgebraClarendon Press, 1963 - 440 pages |
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... determinant . DEFINITION 1.2.2 . The DETERMINANT of the array ( 1.2.1 ) is the number Σ ( λι .... , λη ) άιλι ... απλη ( 1 , ... , λη ) ( 1.2.2 ) where the summation extends over all the n ! arrangements ( 1 , ... , An ) of ( 1 ...
... determinant . DEFINITION 1.2.2 . The DETERMINANT of the array ( 1.2.1 ) is the number Σ ( λι .... , λη ) άιλι ... απλη ( 1 , ... , λη ) ( 1.2.2 ) where the summation extends over all the n ! arrangements ( 1 , ... , An ) of ( 1 ...
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... determinant is a number associated with a square array . However , it is customary to use the term ' determinant ' for the array itself as well as for this number . This usage is ambiguous but convenient , and we shall adopt it since it ...
... determinant is a number associated with a square array . However , it is customary to use the term ' determinant ' for the array itself as well as for this number . This usage is ambiguous but convenient , and we shall adopt it since it ...
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... determinant obtained by interchanging the rth and sth rows in D = | aj | n . Then ‡ ( aj ( i #r ; i 8 ) a'ij = asi ( i = r ) ( ari ( i ( i = 8 ) . Hence , by ... determinant and let D ' I , § 1.2 ELEMENTARY PROPERTIES OF DETERMINANTS 9.
... determinant obtained by interchanging the rth and sth rows in D = | aj | n . Then ‡ ( aj ( i #r ; i 8 ) a'ij = asi ( i = r ) ( ari ( i ( i = 8 ) . Hence , by ... determinant and let D ' I , § 1.2 ELEMENTARY PROPERTIES OF DETERMINANTS 9.
Table des matières
PART | 1 |
VECTOR SPACES AND LINEAR MANIFOLDS | 39 |
THE ALGEBRA OF MATRICES | 72 |
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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