EXISTENCE OF THE HYPERBOLIC SINGULAR VALUE DECOMPOSITION

The hyperbolic singular value decomposition is defined on a general n X m matrix and an m X m signature matrix pair. It is employed in finding the eigenstructure of any matrix that is expressed as the difference of two matrix outer products. Such differences arise in signal processing applications in the context of the covariance differencing. The hyperbolic SVD applies in problems where the conventional SVD cannot be employed. The existence of the hyperbolic singular value decomposition is here extended to the most general case, where neither the general matrix nor the matrix product is assumed full rank.