Related papers: New Representation of Drazin Inverse for Block com…
We present a new method for proving a certain geometric-decay inequality for entries of inverses of B-spline Gram matrices, which is given in [Passenbrunner,Shadrin 2013, arXiv:1308.4824].
We derive new perturbation bounds for eigenvalues of Hermitian matrices with block structures. The structures we consider range from a standard 2-by-2 block form to block tridiagonal and tridigaonal forms. The main idea is the observation…
The sign patterns of inverse doubly-nonnegative matrices are examined. A necessary and sufficient condition is developed for a sign matrix to correspond to an inverse doubly-nonnegative matrix. In addition, for a doubly-nonnegative matrix…
We present new algorithms to detect and correct errors in the product of two matrices, or the inverse of a matrix, over an arbitrary field. Our algorithms do not require any additional information or encoding other than the original inputs…
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…
In this paper we extend notions of the core inverse, core EP inverse, DMP inverse, and CMP inverse over the quaternion skew-field ${\mathbb{H}}$ and get their determinantal representations within the framework of the theory of column-row…
Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix…
We consider a $2\times 2$ system of parabolic equations with first and zeroth coupling and establish a Carleman estimate by extra data of only one component without data of initial values. Then we apply the Carleman estimate to inverse…
Statistical inference for stochastic block models typically relies on the spectrum of the normalized adjacency matrix $\A^*$. In practice, the true probability matrix $\mathbf{B}$ is unknown and must be replaced by a plug-in estimator…
In this paper, we establish a useful set of formulae for the $\sin\Theta$ distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the perturbation of the original matrix propagates into…
In this letter we highlight the inherent problems associted with the inverted hierarchical model of neutrinos with only three generations and suggest possible solutions within the MSSM. we discuss the new parametrisation of the solar mixing…
A novel combinatorial formula is developed for for tensor product multiplicities in representation theory. We introduce a difference formula linking these multiplicities to restricted occupancy coefficients via a shifted operator. This…
We give a formula for matrix exponentials and partial fraction decompositions.
We present both a combinatorial characterization and a recurrent formula for the entries of the inverse Kostka matrix. An application to the topology of the classifying space BU(n) is obtained.
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs…
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…
We introduce twisted matrix factorizations for quantum complete intersections of codimension two. For such an algebra, we show that in a given dimension, almost all the indecomposable modules with bounded minimal projective resolutions…
We prove a modularity lifting theorem for potentially Barostti-Tate representations over totally real fields, generalising recent results of Kisin. Unfortunately, there was an error in the original version of this paper, meaning that we can…
Extending an earlier result for real matrices we show that multiple eigenvalues of a complex matrix lie in a reduced Gershgorin disk. One consequence is a slightly better estimate in the real case. Another one is a geometric application.…
We introduce the Z-polynomial of a matroid, which we define in terms of the Kazhdan-Lusztig polynomial. We then exploit a symmetry of the Z-polynomial to derive a new recursion for Kazhdan-Lusztig coefficients. We solve this recursion,…