# Thread: A few matrix checks

1. ## A few matrix checks

I have 3 eigenvectors for a matrix M, I have normalised them so that U^t*M*U is a diagonal matrix (U^t is the transpose of U).
How do i know which eigenvector goes in which column of U.

Also I have been asked to find the diagonal matrix formed by U^t*M*U.
Is there any way to make this easier to find, as this will require multiplying a lot of fractions with surds everywhere...

2. Originally Posted by deragon999
I have 3 eigenvectors for a matrix M, I have normalised them so that U^t*M*U is a diagonal matrix (U^t is the transpose of U).
How do i know which eigenvector goes in which column of U.

Also I have been asked to find the diagonal matrix formed by U^t*M*U.
Is there any way to make this easier to find, as this will require multiplying a lot of fractions with surds everywhere...
$U^TMU$ will be a diagonal matrix, and the entries along the diagonal will be the eigenvalues of $M$, in whatever order you placed the corresponding eigenvectors in $U$.

3. Thanks, i never knew that.

Does it not matter the order you put the normalised vectors as columns of U then?

4. Originally Posted by deragon999
Thanks, i never knew that.

Does it not matter the order you put the normalised vectors as columns of U then?
No, but the order you put them in will determine the order of the entries of the diagonal matrix, as I explained.