Related papers: Comparisons of Matrices with Different Elements bu…
We study the implications of the existence of two equalities between the elements or cofactors of the neutrino mass matrix. There are sixty five structures of this type for each case. Phenomenological implications for unknown parameters…
For given k distinct complex conjugate pairs, l distinct real numbers, and a given graph G on 2k+l vertices with a matching of size at least k, we will show that there is a real matrix whose eigenvalues are the given numbers and its graph…
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
The existing calculations of the nuclear matrix elements of the neutrinoless double beta-decay differ by about a factor three. This uncertainty prevents quantative interpretation of the results of experiments searching for this process. We…
In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
The product of a Hermitian matrix and a positive semidefinite matrix has only real eigenvalues. We present bounds for sums of eigenvalues of such a product.
In this article, we show multiple inequalities for the singular values of the difference of matrix means. The obtained results refine and complement some well established results in the literature. Although we target singular values…
Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…
Matrix elements of a two-body interaction between states of the jn configutation (n identical nucleons in the j-orbit) are functions of two-body energies. In some cases, diagonal matrix elements are linear combinations of two-body energies.…
A collective description of density matrix is presented for identical multi-level atoms, which are either excited initially, driven coherently or pumped incoherently. The density matrix is defined as expectation value of projection or…
By using the methods of Cauchy-Binet type formula and adjugate matrix respectively, a wonderful equality relating to the elements of eigenvectors, the eigenvalues and the submatrix eigenvalues is proved in arXiv:1908.03795. In the note, we…
If one examines two-body matrix elements from experiment one notices that not only J=0 T=1 lies low but also J=1T=0 and J=J_{max} =2j T=0. It is sometimes thought that one needs both T=1 and T=0 two-body matrix elements to get equally…
We develop several methods, based on the geometric relationship between the eigenspaces of a matrix and its adjoint, for determining whether a square matrix having distinct eigenvalues is unitarily equivalent to a complex symmetric matrix.…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
We obtain eigenvalue equations satisfied by various elliptic modular graphs with five links where two of the vertices are unintegrated. Solving them leads to several non--trivial algebraic identities between these graphs.
We consider path-connected sets of matrices and the induced paths between eigenvalues. We discuss the equivalence relation generated by these paths, and how it relates to the presence of higher multiplicity eigenvalues realized by the set.…
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…
The existing calculations of the nuclear matrix elements of the neutrinoless double $\beta$-decay differ by about a factor three. This uncertainty prevents quantitative interpretation of the results of experiments searching for this…
The calculated nuclear matrix elements for the neutrinoless double-beta ($0\nu\beta\beta$) decay suffer from several limitations. Predicted matrix-element values depend on the many-body method used to calculate them and, in addition, they…
We bring in some new notions associated with $2\times 2$ block positive semidefinite matrices. These notions concern the inequalities between the singular values of the off diagonal blocks and the eigenvalues of the arithmetic mean or…