Fiedler, Miroslav; Markham, Thomas L. On a theorem of Everitt, Thompson, and de Pillis. (English) Zbl 0828.15023 Math. Slovaca 44, No. 4, 441-444 (1994). The main theorem states, that if \(H= (H_{ij})\) is a partitioned positive semidefinite matrix with square blocks, then the matrix \((E_r(H_{ij}))\) is a positive semidefinite matrix, where \(E_r(X)\) denotes the \(r\)th elementary symmetric function in the eigenvalues of \(X\). This result generalizes classical results of W. N. Everitt [Proc. Glasgow Math. Ass. 3, 173-175 (1958; Zbl 0096.008)], R. C. Thompson [Can. Math. Bull. 4, 57-62 (1961; Zbl 0104.012)] and J. de Pillis [Duke Math. J. 36, 511-515 (1969; Zbl 0186.337)]. Reviewer: T.B.Andersen (Aarhus) Cited in 5 ReviewsCited in 8 Documents MSC: 15B57 Hermitian, skew-Hermitian, and related matrices 15A18 Eigenvalues, singular values, and eigenvectors 15A15 Determinants, permanents, traces, other special matrix functions Keywords:partitioned matrix; positive semidefinite matrix; elementary symmetric function; eigenvalues Citations:Zbl 0096.008; Zbl 0104.012; Zbl 0186.337 PDFBibTeX XMLCite \textit{M. Fiedler} and \textit{T. L. Markham}, Math. Slovaca 44, No. 4, 441--444 (1994; Zbl 0828.15023) Full Text: EuDML References: [1] de PILLIS J.: Transformations on partitioned matrices. Duke Math. J. 36 (1969). 511-515. · Zbl 0186.33703 · doi:10.1215/S0012-7094-69-03661-8 [2] EVERITT W. N.: A note on positive definite matrices. Proc. Glasgow Math. Assoc. 3 (1958), 173-175. · Zbl 0096.00804 · doi:10.1017/S2040618500033670 [3] OPPENHEIM A.: Inequalities connected with definite Hermitian forms. J. London Math. Soc. 5 (1930), 114-119. · JFM 56.0106.05 [4] SCHUR I.: Bemerkungen zur Theorie der heschränkten Bilinearformen mit unendlich vielen Veränderlichen. J. Reine Angew. Math. 140 (1911), 1-28. · JFM 42.0367.01 [5] THOMPSON R. C.: A determinantal inequality for positive definite matrices. Canad. Math. Bull. 4 (1961), 57-62. · Zbl 0104.01201 · doi:10.4153/CMB-1961-010-9 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.