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Jan 3, 2011 at 4:27 comment added yaoxiao I see what you have mean,great! I think it is really interesting, when we compare it with the similar claim “every matrix can be decompsed into linear combinations of four orthogonal matrix
Jan 2, 2011 at 20:48 comment added Mikael de la Salle @yaoxiao: the matrix $D$ is hermitian (it is even positive semid-efinite), and every hermitian matrix can be diagonalized in an orthonormal basis.
Jan 2, 2011 at 20:41 comment added yaoxiao thanks for your answering this question. However I still doubt whether the basis E is orthogonal(unitary) basis.
Jan 2, 2011 at 19:48 history edited Mikael de la Salle CC BY-SA 2.5
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Jan 2, 2011 at 19:41 history answered Mikael de la Salle CC BY-SA 2.5