Document Type : Research Paper

Authors

• Maryam Babaei Zarch ¹
• Seyed Abolfazl Shahzadeh Fazeli ¹
• Seyed Mehdi Karbassi ²

¹ Department of Computer Science, Yazd University, Yazd, Iran.

² Department of Mathematical Science, Yazd University, Yazd, Iran.

Abstract

In this  paper, we consider an  inverse eigenvalue problem (IEP) for constructing  a special  kind of acyclic matrices. The problem involves the reconstruction of matrices whose graph is a  banana tree. This is performed by using the  minimal and maximal eigenvalues of all  leading principal submatrices of the required matrix.  The necessary and sufficient conditions
for the solvability of the problem is derived. An algorithm to construct the solution is provided.

Keywords

• Inverse eigenvalue problem
• banana tree
• leading principal minors
• eigenvalue
• graph of a matrix