A System Of Quaternion Tensor Equations With Its Applications

Quaternion,tensor and equation are three important research objects in mathematics.Quaternion was proposed by W.R.Hamilton in 1843.It has important applications in mathematics and practical problems,such as quantum physics,topology,computer science,signal processing,color image processing,face recognition algorithms,image denoising,statistics and so on.In recent years,statistical models based on quaternion theory have been paid attention to and studied.Tensor,also known as hypermatrices,can be used to characterize large-scale and high-dimensional data with complex structures.Therefore,they can play an important role in the big data statistical models.This paper studied the system of quaternion tensor equations via Einstein product We present some necessary and sufficient conditions for the existence of the general solution to this system via Einstein product,and give an expression of the general solution to the system when the solvability conditions are satisfied.As an application,we also present some necessary and sufficient conditions for the existence of a reducible solution to the system and give an expression of the reducible solution to the system when the solvability condi-tions are satisfied.