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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...
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...