Distributions of Demmel and Related Condition Numbers
Distributions of Demmel and Related Condition Numbers
Consider a random matrix $\mathbf{A}\in\mathbb{C}^{m\times n}$ ($m \geq n$) containing independent complex Gaussian entries with zero mean and unit variance, and let $0<\lambda_1\leq \lambda_{2}\leq \cdots\leq \lambda_n<\infty$ denote the eigenvalues of $\mathbf{A}^{*}\mathbf{A}$, where $(\cdot)^*$ represents conjugate-transpose. This paper investigates the distribution of the random variables $\frac{\sum_{j=1}^n \lambda_j}{\lambda_k}$ for $k = 1$ …