# A Condensed Representation of Almost Normal Matrices

Bevilacqua, Roberto and Del Corso, Gianna M. (2012) A Condensed Representation of Almost Normal Matrices. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

In this paper we study the structure of almost normal matrices, that is the matrices for which there exists a rank-one matrix $C$ such that $A^HA-AA^H=CA-AC$. Necessary and sufficient conditions for a matrix to belong to the class are given and a canonical representation as a block tridiagonal matrix is shown. The approach is constructive and in the paper it is explained how, starting from a $1\times 1$ or $2\times 2$ matrix we can generate almost normal matrices. Moreover, given an $n\times n$ almost normal matrix we can compute the block tridiagonal representation with a finite procedure.<br /><br />