# Eigenvalues - real and imaginary

1. Feb 10, 2009

### jpildave

Am I understanding this right?

Let's say I have a 15x15 matrix called Z. Then the matrix of eigenvalues calculated from Z, called D, can have two forms - either diagonal or block diagonal.

If the matrix D comes out with values only on the diagonal, then there are only real values. But, if the matrix D comes out block diagonal, then there are real and imaginary values.

The only reason the matrix D comes out block diagonal is if it is not symmetric, not only in terms of dimensions, but in terms of the actual values in the original matrix Z.

Correct???

2. Feb 12, 2009

### LogicalTime

I believe diagonal is a subset of Jordan block diagonal, since you can count one number as a Jordan block.

Is each entry in Z a real number or complex?

$\left[ \begin{array}{rr} 0&-1\\ 1&0\\ \end{array} \right]$
has eigenvalues = i, -i

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