Canonical forms for symmetric/skew-symmetric real matrix pairs under strict equivalence and congruence
نویسندگان
چکیده
منابع مشابه
Canonical forms for complex matrix congruence and *congruence
Canonical forms for congruence and *congruence of square complex matrices were given by Horn and Sergeichuk in [Linear Algebra Appl. 389 (2004) 347–353], based on Sergeichuk’s paper [Math. USSR, Izvestiya 31 (3) (1988) 481–501], which employed the theory of representations of quivers with involution. We use standard methods of matrix analysis to prove directly that these forms are canonical. Ou...
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We use methods of the general theory of congruence and *congruence for complex matrices—regularization and cosquares—to determine a unitary congruence canonical form (respectively, a unitary *congruence canonical form) for complex matrices A such that ĀA (respectively, A) is normal. As special cases of our canonical forms, we obtain—in a coherent and systematic way—known canonical forms for con...
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Decidability of de nitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of de nitional equality are based on a con uent, strongly-normalizing notion of reduction. Coquand has considered a di erent approach, directly proving the correctness of a practical equivalance algorithm based on the shape o...
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Let V be a q-dimensional vector space. Fix a set B of q(q − 1) monomials in S(V ) of the form x where ik > 0 for all k. The generic element of S(V ) is conjugate under a suitable linear transformation to an element with support off of B. We prove this by showing the existence of a perfect matching with a unique weight in a certain weighted bipartite graph. Such a perfect matching corresponds to...
متن کاملCanonical Forms for Congruence of Matrices: a Tribute To
A canonical form for congruence of matrices was introduced by Turnbull and Aitken in 1932. More than 70 years later, in 2006, another canonical form for congruence has been introduced by Horn and Sergeichuk. The main purpose of this paper is to compare both canonical forms and provide a brief survey on the history of the canonical form for congruence.
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2005
ISSN: 0024-3795
DOI: 10.1016/j.laa.2005.03.035