I have heard of the **Condition Number of a Matrix** in the past and have not paid much attention to this matrix property, until recently. I have been playing with a search algorithm that solves iteratively systems of linear equations. After the basic testing, I moved to more involved testing that uses random matrices. I began to notice that the number of iterations (for a fixed number of equations) varied widely!! I wrote my Matlab and Excel VBA code such that I can watch the progress of conversion to the solution. I noticed that in some cases the solution converged faster than other cases, where the iteration seem to struggle. I first looked at the value of the determinant of the matrix as a possible indicator for how easy or difficult to work with a articular matrix. I then came across internet articles that talked about the condition number of a matrix as being a good indicator for the ease or difficulty of solving linear equations with a matrix [bold]regardless of the algorithm used and the precision of the computation[/bold]. I find this to be somewhat of a revelation since most numerical analysis books rarely mention the condition number of a matrix as an indicator for the level of ease to solve linear equations.

Namir

*Edited: 8 Feb 2012, 9:50 a.m. *