Elliptic equations and products of positive definite matrices | Zendy

Conley Charles H. | Zendy; Pucci Patrizia | Zendy; Serrin James | Zendy

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Elliptic equations and products of positive definite matrices

Author(s) -

Conley Charles H.,

Pucci Patrizia,

Serrin James

Publication year - 2005

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410317

Subject(s) - positive definite matrix , mathematics , hermitian matrix , eigenvalues and eigenvectors , product (mathematics) , pure mathematics , matrix (chemical analysis) , zero (linguistics) , variable (mathematics) , mathematical analysis , combinatorics , geometry , composite material , linguistics , physics , materials science , philosophy , quantum mechanics

We present necessary and sufficient conditions under which the symmetrized product of two n × n positive definite Hermitian matrices is still a positive definite matrix (Part I, Sections 2 and 3). These results are then applied to prove the validity of the strong maximum principle, as well as of the compact support principle, for nonnegative C 1 distribution solutions of general quasilinear inequalities, possibly not elliptic at points where the gradient variable is either zero or large (Part III, Sections 9 and 10). In Part II (Sections 4–8) we consider the general problem of finding bounds for the least and greatest eigenvalues of the product of two (not necessarily definite) Hermitian matrices. In particular, we refine earlier results of Strang for this problem. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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