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Canonical forms for unitary congruence and *congruence [PDF]
Linear and Multilinear Algebra, 2009 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 \bar{A}A (respectively, A^2) is normal.
Vladimir V Sergeichuk
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Some of the next articles are maybe not open access.
Congruences and Unitary Congruences in Matrix Theory
Journal of Mathematical Sciences, 2023This article is a survey about congruence and \(*\)-congruence for complex matrices, with no detailed proofs. The author includes a description of a canonical form for \(*\)-congruence and discusses unitary congruence (including a statement of Youla's theorem on the block triangularization for unitary congruence, and Takagi's theorem stating that every
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Bulletin of the London Mathematical Society, 2004
Wilson's theorem asserts that if \(p\) is a prime and \(n\) is a positive integer, then \((pn)!/(p^nn!)\equiv (-1)^n\pmod p\). In this paper, the authors investigate the above congruence modulo higher powers of \(p\). They prove that if \(p\geq 7\), then the congruence \((pn)!/(p^nn!)\equiv ((p-1)!)^n \pmod{p^{3+\nu_p(n^3-n)}}\) holds, where for a ...
Clarke, Francis, Jones, Christine
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Wilson's theorem asserts that if \(p\) is a prime and \(n\) is a positive integer, then \((pn)!/(p^nn!)\equiv (-1)^n\pmod p\). In this paper, the authors investigate the above congruence modulo higher powers of \(p\). They prove that if \(p\geq 7\), then the congruence \((pn)!/(p^nn!)\equiv ((p-1)!)^n \pmod{p^{3+\nu_p(n^3-n)}}\) holds, where for a ...
Clarke, Francis, Jones, Christine
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Canadian Mathematical Bulletin, 1973
An interesting problem is to discuss the solutions of the congruences in n variables (x)=(xl,…,xn),(1 ...
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An interesting problem is to discuss the solutions of the congruences in n variables (x)=(xl,…,xn),(1 ...
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Psychotherapy, 2011
Congruence or genuineness is a relational quality that has been highly prized throughout the history of psychotherapy, but of diminished research interest in recent years. In this article, we define and provide examples of this attribute of the therapy relationship and present an original meta-analytic review of the empirical literature showing its ...
Gregory G, Kolden +3 more
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Congruence or genuineness is a relational quality that has been highly prized throughout the history of psychotherapy, but of diminished research interest in recent years. In this article, we define and provide examples of this attribute of the therapy relationship and present an original meta-analytic review of the empirical literature showing its ...
Gregory G, Kolden +3 more
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Congruences on *-Regular Semigroups
Periodica Mathematica Hungarica, 2002By a *-regular semigroup \(S\) the authors mean a semigroup with involution * admitting a Moore-Penrose inverse; that is, for each \(a\in S\) there exists a (necessarily unique) solution \(x\) to the equations \(axa=a\), \(xax=x\), \((ax)^*=ax\), \((xa)^*=xa\) which is denoted by \(x=a^+\).
Crvenković, Siniša, Dolinka, Igor
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Bull. EATCS, 1990
We present a proof of a theorem to be found in \textit{H. Ehrig} and \textit{B. Mahr} [Fundamentals of algebraic specifications 1. Berlin etc.: Springer- Verlag, 321 p. (1985; Zbl 0557.68013)]. The theorem states that a relation constructed from a given function is a congruence relation iff that function is a homomorphism: we go on to generalise this ...
Backhouse, R.C., Malcolm, G.R.
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We present a proof of a theorem to be found in \textit{H. Ehrig} and \textit{B. Mahr} [Fundamentals of algebraic specifications 1. Berlin etc.: Springer- Verlag, 321 p. (1985; Zbl 0557.68013)]. The theorem states that a relation constructed from a given function is a congruence relation iff that function is a homomorphism: we go on to generalise this ...
Backhouse, R.C., Malcolm, G.R.
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