On Wikipedia under Statement of Theorem of SVD it says:
Suppose M is an m×n matrix whose entries come from the field K, which is either the field of real numbers or the field of complex numbers. Then there exists a factorization of the form
$$M=U\Sigma V^* $$
where U is an m×m unitary matrix over K, the matrix Σ is an m×n diagonal matrix with nonnegative real numbers on the diagonal, and the n×n unitary matrix V* denotes the conjugate transpose of V. Such a factorization is called the singular value decomposition of M.
Why is it specified that the field K has to be real or complex? Why doesn't it work over a arbitrary field K?