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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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Feature Nonlinear Transformation Non-Negative Matrix Factorization with Kullback-Leibler Divergence
Pattern Recognition, 2022Ning Wu
exaly
Binary Darboux transformation for general matrix mKdV equations and reduced counterparts
Chaos, Solitons and Fractals, 2021Wen-Xiu Ma
exaly
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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