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On the properties of a new tensor product of matrices. (Russian, English) Zbl 1313.15044

Zh. Vychisl. Mat. Mat. Fiz. 54, No. 4, 547- 561 (2014); translation in Comput. Math. Math. Phys. 54, No. 4, 561-574 (2014).
Summary: 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.

MSC:

15A69 Multilinear algebra, tensor calculus
15B34 Boolean and Hadamard matrices
65T50 Numerical methods for discrete and fast Fourier transforms
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