Solutions Of The Quaternion Matrix Equations

In this thesis,the necessary and sufficient conditions for the existences and expressions of the general solutions to two pairs of quaternion matrix equations A₁X₁=C₁,X₂A₂=C₂,A₃X₁B₁+A₄X₂B₂=C_b and X₁A₁=C₁,X₂A₂=C₂,A₃X₁B₁+A₄X₂B₂=C_b are established.Further, the extremal ranks and the least-norm of the general solution to consistent quaternion matrix equations A₁X₁=C₁,X₂A₂=C₂,A₃X₁B₁+A₄X₂B₂=C_b are derived. Using the complex representation of a quaternion matrix,we establish an algorithm of general solution to quaternion matrix equation X³ + AX² +BX+C=0.