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Unified Matrix Treatment of Discrete Transforms
IEEE Transactions on Computers, 1979An unified matrix treatment is developed for some discrete transforms such as Haar (HT), rationalized Haar (RHT), rapid (RT), modified Wash–Hadamard (MWHT), Hadamard– Haar (HHT)r, and rationalized Hadamard–Haar (RHHT)r. For RT a technique for recovering the data sequence from the transform vector is presented.
V. Vlasenko, K. R. Rao
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Matrix differential transformations
Applicable Analysis, 1997Differential transformations can be used in order to transform solutions of a simple differential equation into solutions of a more complicated differential equation. That way one gets explicit representations for solutions of some special differential equations.
H. Florian, J. Püngel, W. Tutschke
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A new method of matrix transformation. I. Matrix diagonalizations via involutional transformations
Journal of Mathematical Physics, 1979It is shown that two matrices A and B of order n×n which satisfy a monic quadratic equation with two roots λ1 and λ2 are connected by ATAB=TABB where TAB=A+B−(λ1+λ2) I with I being the n×n unit matrix (Theorem 1). The condition for TAB to be involutional is that the anticommutator of ?=A−(1/2)(λ1+λ2) I and ?=B−(1/2)(λ1+λ2) is a c number (Theorem 2).
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Matrix Transformations and Factorizations
2017In most applications of linear algebra, problems are solved by transformations of matrices. A given matrix (which represents some transformation of a vector) is itself transformed. The simplest example of this is in solving the linear system Ax = b, where the matrix A represents a transformation of the vector x to the vector b.
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Binary Darboux transformation for general matrix mKdV equations and reduced counterparts
Chaos, Solitons and Fractals, 2021Wen-Xiu Ma
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