An alternative characterization of generalized projectors

✍ Scribed by Jerzy K Baksalary; Xiaoji Liu

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 164 KB
• Volume: 388
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2004.01.010

✦ Synopsis

One of the results of Groß and Trenkler [Linear Algebra Appl. 264 (1997) 463] asserts that a square complex matrix K is a generalized projector if and only if it is (i) quadripotent, (ii) normal, and (iii) partial isometry. The authors supplemented this statement by proving that condition (iii) in the above characterization can actually be deleted. The purpose of the present note is to show that also an alternative reduction of the set of conditions (i)-(iii) is possible as a consequence of establishing the redundancy of (ii) under the presence of (i) and (iii).