In this talk, we will consider some matrix equations and tensor decompositions over the quaternion algebra. We give some necessary and sufficient solvability conditions for some systems of Sylvester-type quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also derive the general solutions to these systems when they are solvable. Moreover, we give some algorithms and numerical examples. We establish some simultaneous decomposition for tensors via different tensor products. These simultaneous decompositions transforms the tensors into some nice forms. We conclude with applications in the color video signal processing and color watermark processing.

12.2.pdf