Prove that the maximal entries of a positive definite, symmetric, real matrix are on the diagonal.
(Algebra by Artin, Edition 2, chapter 8, problem 2.1)
This is an assignment problem so I don't want a complete solution. I'm not really sure what "maximal" means. Can anyone tell me that?
Answer
Since the matrix entries are real, "maximal" here just means largest.
I would interpret the question to mean: given a positive definite real matrix M, let m=max Prove that whenever M_{ij} = m, i=j.
No comments:
Post a Comment