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Given square matrices B and B0 with a poset-indexed block structure (for which an ij block is zero unless i 1 j), when are there invertible matrices U and V with this required-zero-block structure suc...
PATH METHODS FOR STRONG SHIFT EQUIVALENCE OF POSITIVE MATRICES
PATH METHODS STRONG SHIFT EQUIVALENCE POSITIVE MATRICES
2015/9/29
In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring U of R. This paper gives a detailed, unified and gen...
THE APOLLONIAN STRUCTURE OF INTEGER SUPERHARMONIC MATRICES
APOLLONIAN STRUCTURE INTEGER SUPERHARMONIC MATRICES
2015/8/14
We prove that the set of quadratic growths attainable by integervalued superharmonic functions on the lattice Z2 has the structure of an Apollonian circle packing. This completely characterizes the PD...
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
Dense Error Correction Low-Rank Matrices Principal Component Pursuit
2015/6/17
We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been sh...
On the construction of normal mixed difference matrices
Normal mixed difference matrix Kronecker sum
2015/3/18
By exploring the relationship between difference matrices and orthogonal decomposition of projection matrices, this paper presents a general method
for constructing smaller normal mixed difference ma...
Matrices with restricted entries and q-analogues of permutations
Matrices q-analogues of permutations
2010/11/23
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restrict...
Deterministic Compressed Sensing Matrices from Multiplicative Character Sequences
Sensing Matrices Multiplicative Character Sequences
2010/11/18
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is determinist...
Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is s...
A complete unitary similarity invariant for unicellular matrices
invariant unicellular matrices
2010/11/8
Necessary and sufficient conditions for two n-by-n unicellular complex matrices to be unitarily equivalent are established.
Criterion of unitary similarity for upper triangular matrices in general position
upper triangular matrices general position
2010/11/8
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to...
On the eigenvalue problem for a particular class of finite Jacobi matrices
the eigenvalue problem finite Jacobi matrices
2010/11/11
A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first ...
CLT for spectra of submatrices of Wigner random matrices II. Stochastic evolution
CLT submatrices Wigner random matrices II Stochastic evolution
2010/11/22
We show that the global fluctuations of spectra of GOE and GUE matrices and their principal submatrices executing Dyson's Brownian motion are Gaussian in the limit of large matrix dimensions. For nest...
Introduction to the non-asymptotic analysis of random matrices
the non-asymptotic analysis of random matrices math
2010/11/19
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices wi...
Given a large, high-dimensional sample from a spiked population, the top sample covariance eigenvalue is known to exhibit a phase transition. We show that the largest eigenvalues have asymptotic dist...
Adjacency Preserving Bijection Maps of Hermitian Matrices over any Division Ring with an Involution
division ring with involution hermitian matrix adjacency geometry of matrices
2007/12/11
Let $D$ be any division ring with an involution, ${\mathscr H}_n(D)$ be the space of all $n\times n$ hermitian matrices over $D$. Two hermitian matrices $A$ and $B$ are said to be adjacent if ${\rm ra...