I have a set of unitary matrices (four-dimensional, but would like to get an answer in the general case). I get it from singular value decomposition (svd).
There are a lot of matrices, and I began to think about how to store my data in a compressed form. A unitary matrix is a generalization of an orthogonal matrix, which consists of orthonormal bases and describes rotation or reflection. This makes me think that I can store my matrices as a set of angles in complex space, and then restore them fairly accurately.
But when I tried to generalize the formulas for real rotation matrices to the complex case, I got stuck with the concepts of rotation, dot product, and others in the complex case. Therefore, here is my question: is it possible to describe a unitary matrix with a smaller number of complex numbers (it seems to me that it should be 4 complex numbers for a 4x4 matrix), and then restore the original version accurately enough?