On intervals and sets of hypermatrices (tensors) |
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| Authors: | Saeed RAHMATI Mohamed A. TAWHID |
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| Affiliation: | 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 -hypermatrices are uniformly characterized using a finite set of 'extreme' hypermatrices, where 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. |
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| Keywords: | Tensor hypermatrix interval hypermatrix hypermatrix set slice-P-property |
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