It is not uncommon that the covariances of multigroup nuclear data do not obey the sum rules of nuclear data. We present a matrix nearness problem of finding a nearest symmetric matrix with given null vectors and solve it when the distance is measured in the Frobenius norm. The problem appears to be new. We propose that the method should be used to find nearest consistent multigroup covariance matrices with respect to the sum rules of redundant nuclear data.

If the multigroup covariances cannot be easily interpreted in a consistent manner, there is some ambiguity in choosing values for the covariances that are not explicitly mentioned. We present and compare a simple and a heuristic characterization method.

Three practical examples are processed and analyzed: relative covariances of cross sections of 9440Zr and absolute covariances of cross sections of 5024Cr and 23290Th. We demonstrate that satisfactory results can be achieved.

We discuss the properties of the proposed method and the characterization methods and suggest possible improvements. The methods can be used as a part of a quality assurance program and might be valuable additions to nuclear data processing codes.