Let M be a transformation matrix. C is the matrix which diagonalizes M.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to use the formula D = C^{-1}MC. I noticed that depending on how I arrange my vectors in C, I can change the sign of the determinant. If I calculate D using a configuration of C that gives me a negative value for the determinant, my matrix D will have a negative sign in front of the eigenvalues on it's diagonal. (Note: the determinant is needed when calculating the inverse of C, so a negative determinant will multiply the C^{-1}MC equation by -1 )

However, I've read that the matrix D should always have the eigenvalues on it's diagonal, and I've also heard that it doesn't matter how you set-up the matrix C, as long as the eigenvectors are all there.

What's going on? Should I always make sure to use a configuration of C that will get me a positive determinant?

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# Negative determinants when calculating eigenvectors?

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