Estimation of singular values of very large matrices using random sampling

Estimation of Singular Values of Very Large Matri es using Random Sampling

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

On the singular values of random matrices

We present an approach that allows one to bound the largest and smallest singular values of an N × n random matrix with iid rows, distributed according to a measure on R that is supported in a relatively small ball and linear functionals are uniformly bounded in Lp for some p > 8, in a quantitative (non-asymptotic) fashion. Among the outcomes of this approach are optimal estimates of 1±c √ n/N ...

More about measures and Jacobians of singular random matrices

In this work are studied the Jacobians of certain singular transformations and the corresponding measures which support the jacobian computations.

On the singular values of Gaussian random matrices

This short note is about the singular value distribution of Gaussian random matrices (i.e. Gaussian Ensemble or GE) of size N. We present a new approach for deriving the p.d.f. of the singular values directly from the singular value decomposition (SVD) form, which also takes advantage of the rotational invariance of GE and the Lie algebra of the orthogonal group. Our method is direct and more g...