A note on matrices with positive definite real part

London, David

doi:10.1090/S0002-9939-1981-0612711-1

A note on matrices with positive definite real part
HTML articles powered by AMS MathViewer

by David London PDF

Proc. Amer. Math. Soc. 82 (1981), 322-324 Request permission

Abstract:

A lemma characterizing complex matrices with positive definite real part is given. It is shown that many results concerning such matrices are straightforward consequences of this lemma.

References

Ky Fan, Generalized Cayley transforms and strictly dissipative matrices, Linear Algebra Appl. 5 (1972), 155–172. MR 296084, DOI 10.1016/0024-3795(72)90025-0
Ky Fan, On real matrices with positive definite symmetric component, Linear and Multilinear Algebra 1 (1973), no. 1, 1–4. MR 347857, DOI 10.1080/03081087308817001
Shmuel Friedland, Matrices satisfying the van der Waerden conjecture, Linear Algebra Appl. 8 (1974), no. 6, 521–528. MR 453770, DOI 10.1016/0024-3795(74)90086-x

The theory of matrices

Charles R. Johnson, An inequality for matrices whose symmetric part is positive definite, Linear Algebra Appl. 6 (1973), 13–18. MR 311689, DOI 10.1016/0024-3795(73)90003-7
Charles R. Johnson, Inequalities for a complex matrix whose real part is positive definite, Trans. Amer. Math. Soc. 212 (1975), 149–154. MR 424851, DOI 10.1090/S0002-9947-1975-0424851-2
A. M. Ostrowski and Olga Taussky, On the variation of the determinant of a positive definite matrix, Nederl. Akad. Wetensch. Proc. Ser. A. 54 = Indagationes Math. 13 (1951), 383–385. MR 0047597
Olga Taussky, A determinantal inequality of H. P. Robertson. I, J. Washington Acad. Sci. 47 (1957), 263–264. MR 89825