On the properties of a new tensor product of matrices |
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Authors: | M. S. Bespalov |
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Affiliation: | 1. Vladimir State University, ul. Gor’kogo 87, Vladimir, 600000, Russia
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Abstract: | Previously, the author introduced a new tensor product of matrices according to which the matrix of the discrete Walsh-Paley transform can be represented as a power of the second-order discrete Walsh transform matrix H with respect to this product. This power is an analogue of the representation of the Sylvester-Hadamard matrix in the form of a Kronecker power of H. The properties of the new tensor product of matrices are examined and compared with those of the Kronecker product. An algebraic structure with the matrix H used as a generator element and with these two tensor products of matrices is constructed and analyzed. It is shown that the new tensor product operation proposed can be treated as a convenient mathematical language for describing the foundations of discrete Fourier analysis. |
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