ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 12 Dec 2011 05:35:31 -0600Is there a way to block diagonalize a matrix?https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/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?
Sun, 27 Nov 2011 20:30:46 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/Answer by benjaminfjones for <p>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?</p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?answer=12955#post-id-12955How 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.Wed, 30 Nov 2011 11:00:22 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?answer=12955#post-id-12955Comment by Shashank for <p>How do you know that this is possible to do? </p>
<p>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.</p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20784#post-id-20784I know that my matrix block diagonalizable from physics arguments. So can you recommend some place where I can read about it?Wed, 30 Nov 2011 19:57:23 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20784#post-id-20784Comment by benjaminfjones for <p>How do you know that this is possible to do? </p>
<p>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.</p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20722#post-id-20722Can 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. Sun, 11 Dec 2011 09:05:13 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20722#post-id-20722Comment by Shashank for <p>How do you know that this is possible to do? </p>
<p>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.</p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20719#post-id-20719The 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.Mon, 12 Dec 2011 05:35:31 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20719#post-id-20719Answer by torrasque for <p>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?</p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?answer=12990#post-id-12990The inverse of a matrix isn't guaranteed to exists, but there is a function for it anyway.
You can use SciLab's bdiag (numeric). http://help.scilab.org/docs/5.3.2/en_US/bdiag.htmlSat, 10 Dec 2011 05:31:51 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?answer=12990#post-id-12990Comment by benjaminfjones for <p>The inverse of a matrix isn't guaranteed to exists, but there is a function for it anyway.</p>
<p>You can use SciLab's bdiag (numeric). <a href="http://help.scilab.org/docs/5.3.2/en_US/bdiag.html">http://help.scilab.org/docs/5.3.2/en_...</a></p>
https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20723#post-id-20723@chicago is asking about symbolic methods, not numerical.Sun, 11 Dec 2011 09:03:00 -0600https://ask.sagemath.org/question/8503/is-there-a-way-to-block-diagonalize-a-matrix/?comment=20723#post-id-20723