×

A new positive definite geometric mean of two positive definite matrices. (English) Zbl 0872.15014

The authors introduce a new type of geometric mean of two positive definite (under certain conditions, positive semidefinite) matrices and describe its most important properties. This new concept of a geometric mean is also confronted with the mean introduced by T. Ando [Topics on operator inequalities (1978; Zbl 0388.47024)].

MSC:

15A45 Miscellaneous inequalities involving matrices

Citations:

Zbl 0388.47024
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Ando, T., Topics on operator inequalities, (1978), Research Inst. of Applied Electricity, Hokaido Univ Sapporo · Zbl 0388.47024
[2] Ben-Israel, A.; Greville, T.N.E., Generalized inverses: theory and applications, (1974), Wiley New York · Zbl 0305.15001
[3] M. Fiedler and V. Pták, Diagonal blocks of two mutually inverse positive definite block matrices, Czechoslovak Math. J., to appear.
[4] Fitzgerald, C.; Horn, R., On the structure of Hermitian-symmetric inequalities, J. London math. soc., 15, 419-430, (1977) · Zbl 0368.15014
[5] Horn, A., On the eigenvalues of a matrix with prescribed singular values, (), 4-7 · Zbl 0055.00908
[6] Weyl, H., Inequalities between two kinds of eigenvalues of a linear transformation, (), 408-411 · Zbl 0032.38701
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.