Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

Thanks guys for the previous answer, Now suppose if I have a matrix e.g

$$M_1 = \begin{pmatrix} \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} & B \\ B' & D \end{pmatrix}$$ and $M_2$ as

$$M_2 = \begin{pmatrix} \begin{pmatrix} a_{11} & -a_{12} \\ -a_{21} & a_{22} \end{pmatrix} & B \\ B' & D \end{pmatrix}$$

How can i prove for this as eig($M_1$) = eig($M_2$), can this be proven?

share|cite|improve this question

This isn't true. Consider the matrix $$M_1 = \begin{pmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 3 & 3 & 3 \end{pmatrix}$$ with determinant $9$ and $$M_2 = \begin{pmatrix} 1 & -2 & 3 \\ -2 & 1 & 3 \\ 3 & 3 & 3 \end{pmatrix}$$ with determinant $-63$.

share|cite|improve this answer

Your Answer

 
discard

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.