Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have an assignment where I need to create 2x2 matrices for each of the following Eigenvalue pairs.

i) eigenvalues are 2 and -3
ii) eigenvalues are 2+i and 2-i
iii) eigenvalues are 1/2+2i and 1/2-2i

I got the first one just by putting a 0 in one corner and 2 -3 along the diagonal, but I really have no clue how to get an complex number for an eigenvalue. Please someone help me understand!

share|cite|improve this question
Note that 1/2+2i and 1/2-2i are ambiguous. Please use either parentheses or horizontal fraction bars to clarify whether you mean $\frac{1}{2+2i}$ and $\frac{1}{2-2i}$, or $\frac{1}{2}+2i$ and $\frac{1}{2}-2i$. – Jonas Meyer Dec 8 '11 at 5:13
Do you have a restriction on the entries? If not, why not take a matrix that has $2+i$ and $2-i$ in the diagonal, and a zero in one corner? If the entries must be real, note that the characteristic polynomial needs to be $(t-(2+i))(t-(2-i)) = t^2 - 4t + 5$, so fill in your matrix with $a$, $b$, $c$, $d$, compute the characteristic polynomial in terms of $a$, $b$, $c$, and $d$, and find some real solutions to the corresponding equations. – Arturo Magidin Dec 8 '11 at 5:15
yes they have to be real entries. I think this will help tho – NSjonas Dec 8 '11 at 5:18
up vote 2 down vote accepted

It's pretty easy to generate a $2\times 2$ matrix with real entries and conjugate eigenvalues. If you have


then the eigenvalues of this matrix are $a\pm\sqrt{cd}$.

share|cite|improve this answer
Thanks! exactly what I needed! – NSjonas Dec 8 '11 at 5:20

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.