Thread: 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...

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...

will be a diagonal matrix, and the entries along the diagonal will be the eigenvalues of , in whatever order you placed the corresponding eigenvectors in .

Thanks, i never knew that.

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

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.