Crammer007

Dear John Cuther, Thanks a lot for your great idea:) As Dave required, you give a quantitative description. I think it is easy to be applied. Based on your idea, I have a simple example below. Given two vectors (1,0) and (1, 0.0001). Obviously, they are almost parallel vectors and their determinant is 0.0001. If (1,0) is replaced by (10000,0), the determinant is 1. Thus the matrix constructed by the latter vectors is much better than the former. Am I right? Thanks a lot for your guidance:) Crammer007 Dear Dave, Thanks a lot for your great suggestion:) What you suggested is that I want to know. Namely, which quantities can be used for the deciding rule? Please read the reply from John Cuther and D H. They gave great ideas:) Thanks a lot! Crammer007

Dear D H, Thanks a lot for your guidance:) I got your idea but I think the 'maximize' should be replaced by 'as close to zero as possible'. For example, given a pair of orthogonal vectors (0,1) and (1,0), their dot product should be 0*1+1*0=0. Am I right? Thanks a lot for your great help:) Crammer007

Dear all, Would you please give me some guidance on the following simple question? Thanks! Question description: I have a subset of vectors (1 by 3). 3 vectors will be drawn from it to construct a matrix (3*3). Of course, different matrixes will be produced if different 3 vectors are used. Some matrixes are close to singular while some are far away from singularity. My question: What rule can be used to choose 3 vectors which make the matrix far away from singularity? If the subset has 9 vectors (1*3), are there 3 best vectors which can construct a best matrix? How to find the 3 best ones?