Ask Your Question

Is there a way to block diagonalize a matrix?

asked 2011-11-27 20:30:46 -0500

Shashank gravatar image

I am trying to block diagonalize a four by four symbolic matrix in to two matrices of dimension two by two matrices. Is there a simple way to do it in sage?

edit retag flag offensive close merge delete

2 answers

Sort by » oldest newest most voted

answered 2011-11-30 11:00:22 -0500

benjaminfjones gravatar image

How do you know that this is possible to do?

Some 4x4 matrices are not block diagonalizable into 2x2 blocks. For example a nilpotent matrix with a singe Jordan block. If you know for some reason that your symbolic matrix is diagonalizable into 2x2 blocks then probably there is a way to do this, but I don't think possible to write an algorithm that can decide if a symbolic matrix is block diagonalizable.

edit flag offensive delete link more


I know that my matrix block diagonalizable from physics arguments. So can you recommend some place where I can read about it?

Shashank gravatar imageShashank ( 2011-11-30 19:57:23 -0500 )edit

Can you give me an example of a symbolic matrix that is block diagonalizable? Unless the matrix is of a very special form it must depend heavily on assumptions about the domain of the symbolic entries.

benjaminfjones gravatar imagebenjaminfjones ( 2011-12-11 09:05:13 -0500 )edit

The matrix I am trying to block diagonalise is [[Cos(theta),Sin(theta),0,mu],[-Sin(theta),Cos(theta),mu,0],[0,mu,Cos(theta),Sin(theta)],[mu,0,-Sin(theta),Cos(theta)]]. And I am trying to get rid of the mu in the off-diagonal block. I know it is possible because it is a Hamiltonian and I can always go to a basis in which the two systems decouple.

Shashank gravatar imageShashank ( 2011-12-12 05:35:31 -0500 )edit

answered 2011-12-10 05:31:51 -0500

The inverse of a matrix isn't guaranteed to exists, but there is a function for it anyway.

You can use SciLab's bdiag (numeric).

edit flag offensive delete link more


@chicago is asking about symbolic methods, not numerical.

benjaminfjones gravatar imagebenjaminfjones ( 2011-12-11 09:03:00 -0500 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools


Asked: 2011-11-27 20:30:46 -0500

Seen: 1,485 times

Last updated: Dec 10 '11