Finding a diagonal matrix for a given matrix

asked 3 years ago

klaaa gravatar image

Let A be a real n×n matrix. Then there exist orthogonal matrices T1 and T2 such that A=T1DT2 where D is a diagonal matrix with positive entries. D is unique up permutation of the diagonal entries. This decomposition is sometimes called Cartan decomposition.

Question: Is it possible to obtain the matrix D for a given matrix A in Sage?

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2

This might be of some interest for you... as well as this answer.

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 3 years ago )

Not sure but have a look at A.eigenmatrix_left() and eigenmatrix_right() , the eigenvectors are orthogonal and the eigenmatrix is diagonal.

AlanTStafford gravatar imageAlanTStafford ( 3 years ago )