Are eigenvalues of a row-normalized symmetric matrix always real?

[tom08]

Help! Symmetric matrix

I know that all the eigenvalues of a real symmetric matrix are real numbers.
Now can anyone help out how to prove that "all the eigenvalues of a row-normalized real symmetric matrix are real numbers"? Thank you~~~

 

[HallsofIvy]

?? A "row normalized" symmetric matrix is still a symmetric matrix. Just use the same proof as for any symmetric matrix.

 

[CompuChip]

Also note this thread.

 

[aish88]

hi everyone please tell me an algorithm for finding if a matrix is symmetric or not

 

[HallsofIvy]

What's wrong with the obvious one:

Answer= "symmetric"
For i= 1 to n-1
{
For j= i+1 to n
if $a_{ij}\ne a_{ji}$
{
Answer= "not symmetric"
exit loops
}
}
report Answer.