I have a problem when multiplying unitary matrix many times. Initially, a unitary(or symmetric in the following example) matrix is constructed as U. Then I multiply the matrix in an iteractive way and check the unitarity of the results by comparing U*U' with identity. They are close in the first few steps but deviate gradually. Any suggestions to reduce the error and always keep U unitary?

The following is the code.

`clear allM = rand(10);M=0.5*(M+M');U = expm(-1i*M);for t_i = 1:100 U = U*U; norm = trace(U*U'-eye(10))end`

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