In this paper,we use the singular value decomposition of a singular quaternion matrix to(obtain) the exterior differential form of a singular quaternion matrix and then we get the Jacobian of the M-P inverse transformation.

Complex representation of the quaternion matrix equations and structure-preserving algorithm;

Two categories solution of the quaternion matrix equation AX+YA=C and its optimal approximation;

Study of Solutions and Algorithms for Some Quaternion Matrix Equations;

Quaternion and quaternion matrices have been applied in many fields, such as in quantum physics and computer graphics.

By using transformation,the decomposition of quaternion matrices is presented and the equality constrained least squares problem of quaternion matrices with complex presentation and decomposition is studied.

Quaternion matrices and quaternion matrix equations play important roles in quan- tum mechanics.

In recent 30 years, many experts and scholars were carrying on an extensive research about quaternionic matrix and got plenteous theoretical results.

The means to find out M - in a singular matrix and the occasions suitable to the regression were suggested.

Based on the original precise integration method,the problem that singular matrix appeares in non-homogeneous equation was discussed.

LU decomposition is a triangular decomposition approach of non-singular matrix, and the digital image can be seen as a matrix.