Pate, Thomas H. Tensor inequalities, \(\xi\)-functions and inequalities involving immanants. (English) Zbl 0935.15019 Linear Algebra Appl. 295, No. 1-3, 31-59 (1999). This paper improves the result of the author’s recent paper [Proc. Lond. Math. Soc., III. Ser. 76, No. 2, 307-358 (1998; Zbl 0907.15011)]. Using the same notations as in that paper, he shows that permanent dominance holds for all immanants whose associated partitions are of the form \((p,q^2,r)\).Inequalities involving immanants have often been obtained using a \(\Psi\)-function. The results on immanants are obtained by analyzing the \(\xi\)-functions, that are more fundamental than the \(\Psi\)-functions. The \(\xi\)-functions arise from a study of tensor constructions and a special collection of quadratic forms defined on spaces of bi-symmetric tensors. Reviewer: Y.Kuo (Knoxville) Cited in 6 Documents MSC: 15A45 Miscellaneous inequalities involving matrices 15A63 Quadratic and bilinear forms, inner products 15A15 Determinants, permanents, traces, other special matrix functions 15A72 Vector and tensor algebra, theory of invariants Keywords:tensor inequalities; group algebra; generalized matrix function; determinant; immanant inequalities; \(\Psi\)-function; \(\xi\)-functions; permanent dominance; quadratic forms Citations:Zbl 0907.15011 PDFBibTeX XMLCite \textit{T. H. Pate}, Linear Algebra Appl. 295, No. 1--3, 31--59 (1999; Zbl 0935.15019) Full Text: DOI