Interval hypermatrices(tensors)ape 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,a...Interval hypermatrices(tensors)ape 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)Eo-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(P_(0))-hypermatrix.Interval hypermnatrices 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.展开更多
基金The research of the second author was supported by the Natural Sciences and Engineering Research Council of Canada.
文摘Interval hypermatrices(tensors)ape 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)Eo-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(P_(0))-hypermatrix.Interval hypermnatrices 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.
