Simultaneously diagonalizing matrices exactly

asked 2018-01-22 11:43:40 -0600

watson_ladd gravatar image

updated 2018-01-24 15:41:15 -0600

I have a bunch of matrices with integer coefficients that simultaneously commute. I know that there is a basis that simultaneously diagonalizes all of them, and I want to find it exactly so that I can recover all the corresponding eigenvalues as algebraic numbers.

I've tried casting to QQbar and using eigenvectors, but this occasionally tries to divide by zero for no reason I can discern. Any ideas?

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Comments

could you write the code?

vdelecroix gravatar imagevdelecroix ( 2018-01-22 12:21:07 -0600 )edit

Please give us at least two of the many commuting matrices that can be diagonalized (simultaneously).

dan_fulea gravatar imagedan_fulea ( 2018-01-22 14:55:42 -0600 )edit

Let me join the club of asksage junkies : we need your code to understand your problem and (hopefully) provide a solution.

tmonteil gravatar imagetmonteil ( 2018-01-25 04:26:24 -0600 )edit