# Non-zero eigenvalues and square matrix

1. Jun 7, 2010

### Philip Wong

hello,

two quick question here. I've got the answer correct (I think), but I am not too sure how to explain it in words. So I hope someone tell me is my attempted explanation correct.

1) what is the maximum of non-zero eigenvalues a singular square matrix with 7 rows can have?

up to and include 6, because we wee at least 1 eigenvalues that is 0, such that it will give the determinate of the matrix will be 0. Therefore the matrix can be a singular square matrix.

2)how many non-zero eigenvalues does a non-singular square matrix with 5 rows have?
5, because if any eigenvalues in a square matrix is 0, it will turn the matrix into a singular square matrix.

by the way, I need some conformity on the idea, singular square matrix is bringing higher dimension matrix into lower dimension, such that it will not have any inverse right?

2. Jun 7, 2010

### NaturePaper

I think you have missed the word in red :) Ya, both 1 and 2 are correct. However what you ask in the last part, I don't understand it..

3. Jun 7, 2010

### Philip Wong

thanks! so you mean correct, as in my exaplnation was correct right? not just the answer?

don't worry about the last part of my question.

4. Jun 8, 2010

### NaturePaper

Yes, your explanation is correct too.

By the way, these are very much elementary results and there is no confusion that these can be found in all textbooks of matrix theory/linear algebra :)

5. Jun 9, 2010

### Philip Wong

well i'm doing multivariate analysis in statistics, this is part of the topics covered. so i hope i got it corrected