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Full-Text Articles in Physical Sciences and Mathematics
A Permanent Inequality For Positive Semidefinite Matrices, Vehbi Emrah Paksoy
A Permanent Inequality For Positive Semidefinite Matrices, Vehbi Emrah Paksoy
Mathematics Faculty Articles
In this paper, we prove an inequality involving the permanent of a positive semidefinite matrix and its leading submatrices. We obtain a result in the similar spirit of Bapat-Sunder per-max conjecture.
An Update On A Few Permanent Conjectures, Fuzhen Zhang
An Update On A Few Permanent Conjectures, Fuzhen Zhang
Mathematics Faculty Articles
We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture†, Lieb permanent dominance conjecture, Bapat and Sunder conjecture† on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open.We also raise a few new questions for future study. (†conjectures have been recently settled negatively.)
Inequalities Of Generalized Matrix Functions Via Tensor Products, Vehbi Emrah Paksoy, Ramazan Turkmen, Fuzhen Zhang
Inequalities Of Generalized Matrix Functions Via Tensor Products, Vehbi Emrah Paksoy, Ramazan Turkmen, Fuzhen Zhang
Mathematics Faculty Articles
By an embedding approach and through tensor products, some inequalities for generalized matrix functions (of positive semidefinite matrices) associated with any subgroup of the permutation group and any irreducible character of the subgroup are obtained.