Distributions of Demmel and Related Condition Numbers

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tribution of the random variables ∑n j=1 λj λk , for k = 1 and k = 2. These two variables are related to certain condition number metrics, including the so-called Demmel condition number, which have been shown to arise in a variety of applications. For both cases, we derive new exact expressions for the probability densities, and establish the asymptotic behavior as the matrix dimensions grow l...

On the Distribution of a Scaled Condition Number

In this note, we give the exact distribution of a scaled condition number used by Demmel to model the probability that matrix inversion is difficult. Specifically, consider a random matrix A and the scaled condition number kd{A) = \\A\\f \\A~l\\. Demmel provided bounds for the condition number distribution when A has real or complex normally distributed elements. Here, we give the exact formula.

Exact Distributions of Finite Random Matrices and Their Applications to Spectrum Sensing

The exact and simple distributions of finite random matrix theory (FRMT) are critically important for cognitive radio networks (CRNs). In this paper, we unify some existing distributions of the FRMT with the proposed coefficient matrices (vectors) and represent the distributions with the coefficient-based formulations. A coefficient reuse mechanism is studied, i.e., the same coefficient matrice...

Ivestigation of Entropy Generation in 3-D Laminar Forced Convection Flow over a Backward Facing Step with Bleeding

A numerical investigation of entropy generation in laminar forced convection of gas flow over a backward facing step in a horizontal duct under bleeding condition is presented. For calculation of entropy generation from the second law of thermodynamics in a forced convection flow, the velocity and temperature distributions are primary needed. For this purpose, the three-dimensional Cartesian co...

Some New Characterization Results on Exponential and Related Distributions