Corpus ID: 14257218

# The average singular value of a complex random matrix decreases with dimension

@article{Abreu2016TheAS,
title={The average singular value of a complex random matrix decreases with dimension},
author={L. D. Abreu},
journal={ArXiv},
year={2016},
volume={abs/1606.00494}
}
• L. D. Abreu
• Published 2016
• Mathematics, Computer Science
• ArXiv
• We obtain a recurrence relation in $d$ for the average singular value $% \alpha (d)$ of a complex valued $d\times d$\ matrix $\frac{1}{\sqrt{d}}X$ with random i.i.d., N( 0,1) entries, and use it to show that $\alpha (d)$ decreases monotonically with $d$ to the limit given by the Marchenko-Pastur distribution.\ The monotonicity of $\alpha (d)$ has been recently conjectured by Bandeira, Kennedy and Singer in their study of the Little Grothendieck problem over the unitary group \$\mathcal{U}_{d… CONTINUE READING
1 Citations

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