The least-squares solutions of inconsistent matrix equation over symmetric and antipersymmetric matrices

AbstractIn this paper, we are concerned with the following two problems. In Problem I, we describe the set S of real n × n symmetric and antipersymmetric matrices such that minimize the Frobenius norm of LG − E for G, E in Rn × n. In Problem II, we find the unique Ľ in the setsfS, satisfying ∥L∗ − L∥ = minLϵS ∥L∗ − L∥, where L∗ ϵ Rn × n is a given matrix and ∥ · ∥ is the Frobenius norm. We derive a general expression of the set S. For Problem II, we prove the existence and the uniqueness of the solution and provide the expression of this unique solution. We also report some numerical results to support the theory established in the paper