Condition Numbers of Gaussian Random Matrices

• Authors: Zizhong Chen;Jack J. Dongarra
• Venue: SIAM Journal on Matrix Analysis and Applications
• Year: 2005

Let $G_{m \times n}$ be an $m \times n$ real random matrix whose elements are independent and identically distributed standard normal random variables, and let $\kappa_2(G_{m \times n})$ be the 2-norm condition number of $G_{m \times n}$. We prove that, for any $m \geq 2$, $n \geq 2$, and $x \geq |n-m|+1$, $\kappa_2(G_{m \times n})$ satisfies ${\scriptsize \frac{1}{\sqrt{2\pi}}} ( { c }/{x} )^{|n-m|+1} x )}