Related papers: On a decomposition lemma for positive semi-definit…
Semileptonic B and D decays are on a well deserved podium to extract CKM matrix elements, to validate theoretical tools and, more recently, even to look for hints of new physics. Here we review the latest updates.
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
We shall characterize the structure of invertible substitutions on three-letter alphabet. We show that any invertible substitution, after some cyclic operation, can be written as a finite product of permutations and Fibonacci's…
We present some new inequalities related to determinant and trace for positive semidefinite block matrices by using symmetric tensor product, which are extensions of Fiedler-Markham's inequality and Thompson's inequality.
Conjugate partial-symmetric (CPS) tensor is a generalization of Hermitian matrices. For the CPS tensor decomposition some properties are presented. For real CPS tensors in particular, we note the subtle difference from the complex case of…
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
Well-known subadditivity results for positive operators (of Brown-Kosaki and Rotfeld/Ando-Zhan types) are extended to Hermitian and normal ones. Applications to Cartesian decomposition and block-matrices are given.
Two methods to decompose block matrices analogous to Singular Matrix Decomposition are proposed, one yielding the so called economy decomposition, and other yielding the full decomposition. This method is devised to avoid handling matrices…
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay…
This paper discusses further properties of positive partial transpose matrices, with applications towards hyponormal, semi-hyponormal, and $(\alpha,\beta)$-normal matrices. The obtained results present extensions and improvements of many…
The main purpose of this paper is to present a decomposition theorem for nonnegative sesquilinear forms. The key notion is the short of a form to a linear subspace. This is a generalization of the well-known operator short defined by M. G.…
For any real diagonalizable matrix with complex eigenvalues we provide a real, coordinate free decomposition with a clear geometric interpretation.
We introduce a notion of positive definiteness for functions $f\!:P\to\mathbb{R}$ defined on meet semilattices $(P,\preceq,\wedge)$ and prove several properties for these functions. In addition, we utilize the $LDL^{\rm T}$ decomposition of…
The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated…
We give a formula for matrix exponentials and partial fraction decompositions.
We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\ldots,10$. We…
We analyse various exponential off-diagonal decay rates of the elements of infinite matrices and their inverses. It is known that such decay of the elements of an infinite matrix does not imply inverse--closeness, i.e. the inverse, if…
We present a partial characterization of matrices in $M_n(\cA)^+$ satisfying the St{\o}rmer condition.
We prove that over a commutative semiring every symmetric strongly invertible matrix with nonnegative numerical range has a Cholesky decomposition.