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Displaying similar documents to “Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices”

Smallest singular value of sparse random matrices

Alexander E. Litvak, Omar Rivasplata (2012)

Studia Mathematica

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We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances...

Spectral properties of large random matrices with independent entries

P. Dueck, S. O'Rourke, D. Renfrew, A. Soshnikov (2011)

Banach Center Publications

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We consider large Wigner random matrices and related ensembles of real symmetric and Hermitian random matrices. Our results are related to the local spectral properties of these ensembles.

Infinite products of random matrices and repeated interaction dynamics

Laurent Bruneau, Alain Joye, Marco Merkli (2010)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Let be a product of independent, identically distributed random matrices , with the properties that is bounded in , and that has a deterministic (constant) invariant vector. Assume that the probability of having only the simple eigenvalue 1 on the unit circle does not vanish. We show that is the sum of a fluctuating and a decaying process. The latter converges to zero almost surely, exponentially fast as →∞. The fluctuating part converges...

Sparse recovery with pre-Gaussian random matrices

Simon Foucart, Ming-Jun Lai (2010)

Studia Mathematica

Similarity:

For an m × N underdetermined system of linear equations with independent pre-Gaussian random coefficients satisfying simple moment conditions, it is proved that the s-sparse solutions of the system can be found by ℓ₁-minimization under the optimal condition m ≥ csln(eN/s). The main ingredient of the proof is a variation of a classical Restricted Isometry Property, where the inner norm becomes the ℓ₁-norm and the outer norm depends on probability distributions.

Pentadiagonal Companion Matrices

Brydon Eastman, Kevin N. Vander Meulen (2016)

Special Matrices

Similarity:

The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...

The random paving property for uniformly bounded matrices

Joel A. Tropp (2008)

Studia Mathematica

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This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison-Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original...