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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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Spectral Density Matrix Transformations
Journal of the IEST, 2017Abstract Reference criteria for a multiple degree-of-freedom (MDOF) random vibration test is generally provided in terms of an acceleration-based spectral density matrix (SDM). This SDM may be developed in terms of the auto-spectral densities (ASDs) and cross-spectral densities (CSDs) computed from the time histories acquired from an ...
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Applied Mathematics and Computation, 1984
The Laguerre transform, introduced by \textit{J. Keilson} and \textit{W. R. Nunn} [ibid. 5, 313-359 (1979; Zbl 0449.65086)], \textit{J. Keilson}, \textit{W. R. Nunn} and the author [ibid. 8, 137-174 (1981; Zbl 0457.42011)], and further studied by the author [Development of the Laguerre transform method for numerical exploration of applied probability ...
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The Laguerre transform, introduced by \textit{J. Keilson} and \textit{W. R. Nunn} [ibid. 5, 313-359 (1979; Zbl 0449.65086)], \textit{J. Keilson}, \textit{W. R. Nunn} and the author [ibid. 8, 137-174 (1981; Zbl 0457.42011)], and further studied by the author [Development of the Laguerre transform method for numerical exploration of applied probability ...
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Matrix Equations and Transformations
1986In this chapter we consider solutions of a linear set of equations using some of the concepts discussed in Chapter 4. In addition, we introduce the concepts of a vector space, rank of a matrix, and so on. We end the chapter with a discussion of various transformations that are popular in the digital signal processing area.
John E. Hershey, R. K. Rao Yarlagadda
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The Matrix Transform Processor
IEEE Transactions on Computers, 1976A matrix transform processor (MTP) for an Evans and Sutherland LDS-2 graphics system has been designed and built at the University of North Carolina. The MTP performs all the important functions of a matrix multiplier, clipper, and perspective divider.
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
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