BOUNDS ON CONDITION NUMBER OF MATRIX

Let ||x||be a norm defined on linear space C~m, then a matrix A∈C, as a linear operator on C~n, has a norm correspondingly. We denote by P(A) the condition number of A, namely P(A) = |A||A|. This is a basic concept in numerical algebra and also very important in some other fields of numerical analysis. Under certain circumstances, someone takes the ratio |λ|/|λ| as the condition number, where λand λare the largest and smallest eigenvalue of A by norm. The relationship between them will be presented below.