Talk:Diagonal matrix

In the last section, Uses, some confusion arises regarding the different meanings of "unitarily equivalent" and "unitarily similar".

I am fairly confident that the spectral theorem states that a normal matrix is unitarily equivalent to a diagonal matrix, with unitarily equivalent defined as follows:

A square matrix A is considered unitarily equivalent to a matrix B if there exists a unitary matrix U that satisfies A=UBU^\dagger, where U^\dagger means taking the complex conjugate of the transpose of U.

Now, an mxn matrix A is considered unitarily similar to an mxn matrix B if there exist two unitary matrices U (nxn) and T (mxm) satisfying A=TBU^\dagger. This definition plays a role in the cited singular value decomposition theorem.

So I'd prefer to see the two terms swap places, if people can agree on using the words with the meaning outlined above.