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Vectors of a square matrix in \({\mathbb R}^n\). (English) Zbl 1303.15033

Summary: The purpose of this paper is to introduce that an arbitrary non-singular \(n\)-th order square matrix can be represented as a matrix associated with an arbitrary versor lying in the \(n\)-dimensional Cartesian space in such a way that the successive terms of this matrix are the products of the coordinates of this versor and the corresponding \(n\) coordinates of different vectors lying in the same space. We next demonstrated that if the versor is one of the eigenversors of matrix, then the direction of it determines the distance, while the eigenvalue is equal to the distance of the plane defined by these vectors from the origin. Finally, the paper presents selected examples for the matrix of the second and third row.

MSC:

15A69 Multilinear algebra, tensor calculus
15A18 Eigenvalues, singular values, and eigenvectors
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