WITHDRAWN: Similarity reduction of matrix over a quaternion division ring

✍ Scribed by Li-Ping Huang; Zhuo-Jun Liu

• Book ID: 104037169
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 385 KB
• Volume: 428
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/j.laa.2007.08.006

✦ Synopsis

Let F be a field of characteristic / =2, H F = a,b F the quaternion division ring over F . This paper discusses the similarity of polynomials over H F . By using polynomials over H F , this paper proves that every square matrix over H F is similar to a uniquely generalized Jordan canonical form, and a quaternion matrix A is similar to a matrix over F if and only if A is similar to A * via a Hermite similarity transformation, or if and only if A is product of two quaternion Hermite matrices.