Gauss sums and the number of solutions to the matrix equation over
Philip Buckhiester (1973)
Acta Arithmetica
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Philip Buckhiester (1973)
Acta Arithmetica
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Jacob Beard, Robert Mcconnel (1982)
Acta Arithmetica
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Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)
Open Mathematics
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Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.
Jiří Seitz (1966)
Časopis pro pěstování matematiky
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Ioannis K. Argyros (1988)
Mathematica Slovaca
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Jiří Gregor (1981)
Aplikace matematiky
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Homogeneous quadratic polynomials in complex variables are investigated and various necessary and sufficient conditions are given for to be nonzero in the set . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.