The left and right inverse eigenvalue problems of generalized reflexive and anti-reflexive matrices

The inverse eigenvalue problem for a Hermitian reflexive matrix and the optimization problem

“…Recently, some specific problems have been tackled [9,10,11,14]. In particular, a similar problem has been treated in [13] solved by different techniques than those used in this paper.…”

“…Also, for structured matrices such as Toeplitz and generalized K-centrohermitian, problems like these ones have been studied in [6,7]. For a left and right inverse eigenvalue problem with reflections we can refer to [11]. The problem treated in this paper extends all these known cases in the literature related to reflexivity.…”

Left and Right Inverse Eigenpairs Problem of Orthogonal Matrices

“…Different matrix set can lead to different left and right inverse eigenpairs problems, such as, Zhang's [4], Li's [5][6][7], Liang's [8] have considered, respectively, the left and right inverse eigenpairs problem of real matrices, skew-centrosymmetric matrices, generalized centrosymmetric matrices, symmetrizable matrices and generalized reflexive and anti-reflexive matrices, and the explicit expressions of the solutions have been obtained. In this paper, we considered the left and right inverse eigenpairs problem of orthogonal matrices (namely Problem I) and its optimal approximation problem (namely Problem II).…”

“…We obtain the optimal approximate solution with the properties of continuous function in bounded closed set. Compare the problems in [4][5][6][7][8] (those matrix sets are subspace), the bounded closed set problems we discussed in this paper are a new class of left and right inverse eigenpairs problems.…”

“…In this paper, we will discuss this problem. The orthogonal matrix set is a bounded closed set, while those matrix sets in [4][5][6][7][8] are subspace. The left and right inverse eigenpairs problems and it's optimal approximation problems for bounded closed set are a new class of left and right inverse eigenpairs problems.…”