The elements of a given n-dimensional
vector XRn, n=2m, mN are used to build matrices of transpositions (Tr
matrices), which are a particular instance of symmetric matrices. Tr matrices
have been shown to be both symmetric and persymmetric. As a Hadamard product of
Tr matrix and matrix, a new approach for creating transposition matrices with
mutually orthogonal rows (Trs matrices) of dimensions 2, 4, and 8 has been
presented. Hadamard, and their use in QR decomposition and n-dimensional
rotation matrix production has been examined. Obtaining an orthogonal Trs
matrix of sizes 4 and 8 that rotates a given vector to the direction of one of
the coordinate axes takes less processing time than obtaining a Housholder
matrix of the same size, according to tests and analysis of the technique. The
Tr and Trs matrices are so useful in matrix calculations.
Author (S) Details
Dr.
Ognyan Ivanov Zhelezov
Nikola
Vaptsarov Naval Academy, Varna, 9000, Bulgaria.
View Book :- https://stm.bookpi.org/CTMCS-V6/article/view/2583
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