Potęga macierzy Toeplitza
Abstrakt
W artykule będziemy rozpatrywać macierze Toeplitza odnosząc się do ich ciekawej struktury. Zwrócimy uwagę na to, że nie zawsze potęga macierzy Toeplitza będzie macierzą Toeplitza. Przytoczymy i przeanalizujemy z [3] warunek konieczny i wystarczający na to, aby każda dodatnia i całkowita potęga macierzy Toeplitza była macierzą Toeplitza.
The power of Toeplitz matrix
In the article we will consider the Toeplitz matrices refer to their interesting structure. We will draw attention to the fact that the powers of a Toeplitz matrix is not necessarily Toeplitz matrix. We will cite and analyze from [3] the necessary and sufficient condition, that all positive integer powers of a Toeplitz matrix is still Toeplitz matrices.
The power of Toeplitz matrix
In the article we will consider the Toeplitz matrices refer to their interesting structure. We will draw attention to the fact that the powers of a Toeplitz matrix is not necessarily Toeplitz matrix. We will cite and analyze from [3] the necessary and sufficient condition, that all positive integer powers of a Toeplitz matrix is still Toeplitz matrices.
Bibliografia
R. M. Gray, "Teoplitz and circulant matrices: a review", Print version of Foundations and Trends in Communications and Information Theory Vol. 2, No. 3 (2005), Zbl~1115.15021.
R. A. Horn, C. R. Johnson, "Matrix Analysis", Cambridge University Press, Cambridge, 1985. MR 2978290, Zbl 1267.15001.
H. Wu, "On Positive Integer Powers of Toeplitz Matrices", Journal of Mathematics Research 4 (2013), 52-57.
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