Mathematical models can solve problems to find out which individuals are superior from crosses in the field of genetics. The matrix form of the mathematical model using the concept of matrix diagonalization can solve these problems. The general definition of matrix diagonalization is with the diagonalized matrix elements obtained from the probability of crossing the average parent and the recessive parent. The mathematical model of a cross between the average parent and recessive parent can be formulated as . The behavior of the solution from the cross is in the form of an explicit equation which can be formulated as . From the calculation results, it is found that in the nth generation, where the limit for n goes to infinity, all offspring from crossing normal parents with offspring with genotypes are normal genotypes. In contrast, all offspring from crossing recessive parents with offspring with genotypes are heterozygous.

Included in

Mathematics Commons