Monday, 4 February 2013

linear algebra - Prove that the maximal entries of a positive definite, symmetric, real matrix are on the diagonal




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

real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

How to find \lim_{h\rightarrow 0}\frac{\sin(ha)}{h} without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...