On the sum of normal matrices

TL;DR

This paper revisits Djoković's classic result on the sum of normal matrices, connects it to Semrl's work, and extends the Craig-Sakamoto theorem to multiple normal matrices, providing new insights in matrix theory.

Contribution

It extends the Craig-Sakamoto theorem to the sum of two or more normal matrices using Djoković's result and highlights connections to Semrl's work.

Findings

Extended Craig-Sakamoto theorem to multiple normal matrices

Connected Djoković's result with Semrl's work

Provided commentary on a recent mathematical problem

Abstract

This short paper revisits a remarkable but almost overlooked result of Djokovi\'{c} [Proc. Amer. Math. Soc. 27 (1971) 19-23]. A connection to a result of \u{S}emrl is pointed out. With Djokovi\'{c}'s result, an extension of Craig-Sakamoto theorem to $k$ ($k\ge 2$) normal matrices is presented. A comment to a recent monthly problem is also given.