Matrix divisibility sequences
Gunther Cornelissen, Jonathan Reynolds (2012)
Acta Arithmetica
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Gunther Cornelissen, Jonathan Reynolds (2012)
Acta Arithmetica
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P. D. Johnson Jr., R. N. Mohapatra (1985)
Annales Polonici Mathematici
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R. Ben Taher, M. Rachidi (2015)
Special Matrices
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We present a constructive procedure for establishing explicit formulas of the constituents matrices. Our approach is based on the tools and techniques from the theory of generalized Fibonacci sequences. Some connections with other results are supplied. Furthermore,we manage to provide tractable expressions for the matrix functions, and for illustration purposes we establish compact formulas for both the matrix logarithm and the matrix pth root. Some examples are also provided. ...
Tripathy, B.C. (1998)
Bulletin of the Malaysian Mathematical Society. Second Series
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João Lita da Silva, António Manuel Oliveira (2009)
Discussiones Mathematicae Probability and Statistics
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A matrix generalization of Kronecker's lemma is presented with assumptions that make it possible not only the unboundedness of the condition number considered by Anderson and Moore (1976) but also other sequences of real matrices, not necessarily monotone increasing, symmetric and nonnegative definite. A useful matrix decomposition and a well-known equivalent result about convergent series are used in this generalization.
Karol Pak, Andrzej Trybulec (2007)
Formalized Mathematics
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In the article the formula for Laplace expansion is proved.
Mazanik, S.A. (1998)
Memoirs on Differential Equations and Mathematical Physics
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Bo Zhang, Yatsuka Nakamura (2006)
Formalized Mathematics
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In this article, we first define finite sequences of probability distribution and matrices of joint probability and conditional probability. We discuss also the concept of marginal probability. Further, we describe some theorems of matrices of real elements including quadratic form.
Larsen, Michael (1995)
The Electronic Journal of Combinatorics [electronic only]
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Janaki, T.M., Rangarajan, Govindan (2003)
International Journal of Mathematics and Mathematical Sciences
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Al'pin, Yu.A., Ilyin, S.N. (2005)
Zapiski Nauchnykh Seminarov POMI
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Branislav Martić (1984)
Publications de l'Institut Mathématique
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