On intervals and sets of hypermatrices (tensors)

doi:10.1007/s11464-020-0884-3

Front. Math. China

2020, Vol. 15

Issue (6) : 1175-1188 https://doi.org/10.1007/s11464-020-0884-3

RESEARCH ARTICLE

On intervals and sets of hypermatrices (tensors)

Saeed RAHMATI(

), Mohamed A. TAWHID

Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC V2C 0C8, Canada

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Abstract

Interval hypermatrices (tensors) are introduced and interval $α$ -hypermatrices are uniformly characterized using a finite set of 'extreme' hypermatrices, where $α$ can be strong P, semi-positive, or positive definite, among many others. It is shown that a symmetric interval is an interval (strictly) copositive-hypermatrix if and only if it is an interval (E) E₀-hypermatrix. It is also shown that an even-order, symmetric interval is an interval positive (semi-) definite-hypermatrix if and only if it is an interval P (P₀)-hypermatrix. Interval hypermatrices are generalized to sets of hyper-matrices, several slice-properties of a set of hypermatrices are introduced and sets of hypermatrices with various slice-properties are uniformly characterized. As a consequence, several slice-properties of a compact, convex set of hyper-matrices are characterized by its extreme points.

Keywords Tensor hypermatrix interval hypermatrix hypermatrix set slice-P-property

Corresponding Author(s): Saeed RAHMATI

Issue Date: 05 February 2021

Cite this article:

Saeed RAHMATI,Mohamed A. TAWHID. On intervals and sets of hypermatrices (tensors)[J]. Front. Math. China, 2020, 15(6): 1175-1188.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0884-3
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I6/1175

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