Abstract:
In this work, the inverse eigenvalue problem is studied in the context of singular
symmetric and Hermitian matrices, with a particular emphasis on ranks five
and six. We looked into ways to solve singular symmetric and Hermitian matrices’
Inverse Eigenvalue Problem (IEP). We devised a method to reconstruct
such matrices from their eigenvalues, based on a solvability lemma. Through
innovative methodologies, we aim to provide effective solutions for determining
the original matrices from their eigenvalues, shedding light on challenges
posed by singularity and higher rank. In the case of n × n matrix, the number
of independent matrix elements would reduced
