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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.
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker
Mathematics Faculty Articles
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete …
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.
On The Null Space Structure Associated With Trees And Cycles, Shaun M. Fallat, Shahla Nasserasr
On The Null Space Structure Associated With Trees And Cycles, Shaun M. Fallat, Shahla Nasserasr
Mathematics Faculty Articles
In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in the case of trees, and seems to represent a unifying theory within the context of the support of the null space. We extend this idea and apply it to describe the null vectors and corresponding nullities of certain symmetric matrices associated with cycles