Least squares Hermitian solution of the matrix equation with the least norm over the skew field of quaternions

详细信息	查看全文 | 推荐本文 |

• 作者：Shifang Yuan ; Anping Liao ; Yuan Lei
• 关键词：Matrix equation ; Least squares solution ; Moore– ; Penrose generalized inverse ; Kronecker product ; Quaternion matrices
• 刊名：Mathematical and Computer Modelling
• 出版年：2008
• 期刊代码：86_08957177
• 类别：cp
• 出版时间：July 2008
• 卷：48
• 期：1-2
• 页码：91-100
• 文件大小：249 K

摘要

By using the complex representations of quaternion matrices, Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expression of the least squares Hermitian solution of the matrix equation cd993ecdde3d682297818974f47" title="Click to view the MathML source" alt="Click to view the MathML source">(AXB,CXD)=(E,F) with the least norm over the skew field of quaternions, and provide a numerical algorithm to calculate the forementioned solution.