摘要
Let ||x||μ be a norm defined on linear space Cm, then a matrix A∈Cm×n, as a linear operator on Cn, has a norm correspondingly. We denote by Pμ （A） the condition number of A, namely Pμ（A） = |A|μ|A-1|μ. 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 |λz|/|λ1| as the condition number, where λm and λ1 are the largest and smallest eigenvalue of A by norm. The relationship between them will be presented below.
