| Quaternion was found by Hamilton, a British mathematician in 1843.The quaternion and the matrix theory method has wide spread and important apply in aspects of algebra, geometry, physics, engineering technology,but it is studies the quantum mechanics the important tool.The quaternion matrix equation is studies in the quaternion quantum-mechanical theory of the corresponding mathematics physical model foundation. As a result of quaternion multiplication non-exchangeability, Causes some quaternion number matrix equation to be very difficult to solve.therefore, Studies the quaternion linear matrix equation solution question is in a matrix theory kind of important question under the non-exchange significance.This paper studies linear quaternion matrix equation problem. First,it introduces quaternion and matrix related concept and the theoretical knowledge on the content, and introduces the quaternion matrix's duplicate expression, obtains the quaternion system of linear equations's solution existence theorem and the related solution form;then using quaternion matrix duplicate expression and direct product and the matrix method to straighten the quaternion matrix equation into linear equations,thus it obtained the linear quaternion matrix equaternion related conditions and the nature of the solvability,it is introduction of a regular matrix and the concept of j conjugate matrix,and discuss the relate properties,it is use j conjugate matrix knowledge turn solve the complex matrix equation into the quaternion matrix equation,at the same time,the method is given. Finally by extending the quaternion matrix equation ABX=C to the generalized quaternion matrix equationΣAiXBi=C.Parts of the text are given in the relevant example. |
