Characterizations of complex P-matrices

Characterizations of complex P-matrices

A P-matrix is a square matrix all of whose principal minors are positive. The characterization of real P-matrices as matrices that do not reverse the sign of any nonzero real vector is generalized to complex P-matrices by associating them with the reflection of complex vectors. This prompts the exte...

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Veröffentlicht in:The Electronic journal of linear algebra 2024-10, Vol.40, p.682-691
Hauptverfasser: Tsatsomeros, Michael, Olesky, Dale, Van den Driessche, Pauline
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description A P-matrix is a square matrix all of whose principal minors are positive. The characterization of real P-matrices as matrices that do not reverse the sign of any nonzero real vector is generalized to complex P-matrices by associating them with the reflection of complex vectors. This prompts the extension of other P-matrix properties and related real matrix classes to the complex field. In particular, semipositivity of real P-matrices is generalized to complex P-matrices. Principal pivot transforms and Cayley transforms of complex P-matrices are also considered.
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