![]() In inexact arithmetic, the condition number is pretty much the only nice diagnostic you have.įor applications, the choice of condition number usually does not matter much, since if some matrix $\mathbf A$ has a large/small $p$-norm condition number, the $q$-norm condition number of the same matrix will be of comparable magnitude. Now, why should we be interested in this condition number? One for instance cannot depend on the determinant, as it is not a reliable measure of how badly a coefficient matrix will behave in a linear system (see also this answer). One then speaks of the "2-norm condition number", $\kappa_2(\mathbf A)$, the "$\infty$-norm condition number", $\kappa_\infty(\mathbf A)$. This is usually associated with a matrix $\mathbf A$ that figures as the matrix of coefficients in the linear system, and thus, we have the symbol $\kappa(\mathbf A)$.įurther, there is not just one condition number, but a number of them, all dependent on the underlying matrix norm used in their definition. M.Īs already mentioned, there is this quantity of great interest to people in the business of solving simultaneous linear equations, called the condition number, and conventionally denoted by the symbol $\kappa$. This might be as good a time as any to distill the collective wisdom of Messrs. ![]()
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