A basic decomposition result related to the notion of the rank of a matrix and applications.
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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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.
Chao Ma (2017)
Open Mathematics
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Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Tian, Yongge, Cheng, Shizhen (2003)
The New York Journal of Mathematics [electronic only]
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Stanimirović, P. (1996)
Matematichki Vesnik
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Jitka Machalová (2000)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Wang, Qing-Wen, Zhang, Hua-Sheng, Yu, Shao-Wen (2008)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Bapat, R.B., Zheng, Bing (2003)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Meenakshi, Ar., Anandam, N. (1992)
International Journal of Mathematics and Mathematical Sciences
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Arthur Kennedy-Cochran-Patrick, Sergeĭ Sergeev, Štefan Berežný (2019)
Kybernetika
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We consider inhomogeneous matrix products over max-plus algebra, where the matrices in the product satisfy certain assumptions under which the matrix products of sufficient length are rank-one, as it was shown in [6] (Shue, Anderson, Dey 1998). We establish a bound on the transient after which any product of matrices whose length exceeds that bound becomes rank-one.