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Generating Totally Positive Toeplitz Matrix from an Upper Bidiagonal Matrix
Department of Mathematics, Faculty of Science, Menoufia University, Al Minufya, Egypt
Department of Mathematics, Faculty of Science, Zagazig University, Ash Sharqiyah, Egypt
- 1 Department of Mathematics, Faculty of Science, Menoufia University, Al Minufya, Egypt
- 2 Department of Mathematics, Faculty of Science, Zagazig University, Ash Sharqiyah, Egypt
Advances in Linear Algebra & Matrix Theory·Volume 05 (2015)·Pages 143–149·Published 19 November 2015·DOI10.4236/alamt.2015.54014
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Abstract
In this paper, we construct one of the forms of totally positive Toeplitz matrices from upper or lower bidiagonal totally nonnegative matrix. In addition, some properties related to this matrix involving its factorization are presented.
KeywordsTotally Positive MatrixTotally Nonnegative MatrixToeplitz Matrix<i>LU</i>Factorization
- Ando, T. (1987) Totally Positive Matrices. Linear Algebra and its Applications, 90, 165-219. http://dx.doi.org/10.1016/0024-3795(87)90313-2
- Fallat, S.M. (2007) Totally Positive and Totally Nonnegative Matrices. Chapter 21 in Handbook of Linear Algebra, In: Hogben, L., Ed., Chapman & Hall/CRC, Boca Raton.
- Pinkus, A. (2010) Totally Positive Matrices, Cambridge Tracts. Vol.181, Cambridge Univ. Press, Cambridge.
- Fallat, S.M. and Johnson, C.R. (2011) Totally Nonnegative Matrices, Princeton Ser. Appl. Math. Princeton University Press, Princeton, Oxford.
- Cryer, C.W. (1973) The LU-Factorization of Totally Positive Matrices. Linear Algebra and its Applications, 7, 83-92. http://dx.doi.org/10.1016/0024-3795(73)90039-6
- Fallat, S.M. (2001) Bidiagonal Factorizations of Totally Nonnegative Matrices. American Mathematical Monthly, 108, 697-712. http://dx.doi.org/10.2307/2695613
- Adm, M. and Garloff, J. (2013) Interval of Totally Nonnegative Matrices. Linear Algebra and its Applications, 439, 3796-3806.