Inverse of a Matrix of Relationships Due to Sires and Maternal Grandsires

Abstract

The most important identifiable relationships among sires used in artificial insemination are due to common sires and maternal grandsires. A rapid method for finding the inverse of a numerator relationship matrix resulting from use of these two points in the pedigree has been developed. As a consequence, relationships among all sires to be evaluated can be incorporated easily into best linear unbiased prediction of future progeny of these sires.