Non-zero eigenvalues and square matrix

[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?

 

[NaturePaper]

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

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..

 

[Philip Wong]

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..

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.

 

[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 :)

 

[Philip Wong]

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