Finding a diagonal matrix for a given matrix

asked 2021-06-09 14:00:12 +0100

klaaa gravatar image

Let $A$ be a real $n \times n$ matrix. Then there exist orthogonal matrices $T_1$ and $T_2$ such that $A=T_1 D T_2$ 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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This might be of some interest for you... as well as this answer.

Emmanuel Charpentier gravatar imageEmmanuel Charpentier ( 2021-06-09 16:03:50 +0100 )edit

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 ( 2021-06-26 15:55:48 +0100 )edit
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