Asignificant amount of elegant work has been accomplished in the study of partial isometries. In this article, weintroduce a new class of operators, referred to as the (k,m,n)-partial isometries, which extends the concept of partial isometry. We delve into the most intriguing outcomes related to this class by extending previously established results for partial isometries and by exploring new results on partial isometries. We investigate the relationship of this new class of operators with classical notions of operators, such as partial isometries, power partial isometries, paranormal, semi-regular, and quasi-Fredholm. Additionally, we examine some fundamental properties and structure theorems of (k,m,n)-partial isometries. Furthermore, we provide spectral properties of (k,m,n)-partial isometries.

Our aim in this paper is to determine when a partially isometric matrix is normal. However, we do not restrict ourselves to the finite-dimensional case and we describe when a partial isometry in ℬ ⁢ ( ℋ ) satisfies several strong and weak normal properties. In particular, we give elegant characterisations of normal partial isometries on infinite-dimensional Hilbert Spaces in terms of generalized inverses; we collect some spectral properties and explore when an operator in ℬ ⁢ ( ℋ ) is similar to a normal partial isometry. We close the paper by treating when a partial isometry is hyponormal.