Matrices similar to partial isometries

Abstract

Abstract. We determine when a matrix is similar to a partial isometry, refining a result of Halmos-McLaughlin.

Partially isometric matrices: a brief and selective survey

“…In this section we consider similarity invariants, such as the spectrum, characteristic polynomial, and Jordan canonical form, of partial isometries. Among other things, we discuss a recent result of the first author and David Sherman, who solved the similarity problem for partially isometric matrices [11].…”

“…There is another proof, which appeared in [11], of Theorem 4.2 that is of independent interest because of its critical use of the Weyl-Horn inequalities [21,32]. 2 Theorem 4.4.…”

“…The following theorem is due to the first author and David Sherman [11]. The proof requires several lemmas and is deferred until the end of this section.…”