Inequalities for a complex matrix whose real part is positive definite

Author:
Charles R. Johnson

Journal:
Trans. Amer. Math. Soc. **212** (1975), 149-154

MSC:
Primary 15A45

MathSciNet review:
0424851

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Denote the real part of by . We provide dual inequalities relating and and an identity between two functions of *A* when *A* satisfies . As an application we give an inequality (for matrices *A* satisfying ) which generalizes Hadamard's determinantal inequality for positive definite matrices.

**[1]**C. R. DePrima and C. R. Johnson,*The range of 𝐴⁻¹𝐴* in 𝐺𝐿(𝑛,𝐶)*, Linear Algebra and Appl.**9**(1974), 209–222. MR**0361862****[2]**Ky Fan,*Generalized Cayley transforms and strictly dissipative matrices*, Linear Algebra and Appl.**5**(1972), 155–172. MR**0296084****[3]**Ky Fan,*On real matrices with positive definite symmetric component*, Linear and Multilinear Algebra**1**(1973), no. 1, 1–4. MR**0347857****[4]**Charles R. Johnson,*An inequality for matrices whose symmetric part is positive definite*, Linear Algebra and Appl.**6**(1973), 13–18. MR**0311689****[5]**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**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
15A45

Retrieve articles in all journals with MSC: 15A45

Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1975-0424851-2

Keywords:
Eigenvalues,
Hadamard inequality,
real part,
positive definite

Article copyright:
© Copyright 1975
American Mathematical Society