Research On The Generalized Inverses Of Quaternion Tensors

This dissertation mainly studies the specific definitions,properties and calculation algorithm of the generalized inverses of quaternion tensors.And a Gauss-Jordan elimination method for calculating WG inverse is also studied.The full text is divided into four parts.In the first part,we introduce the research background of the generalized inverses of quaternion tensors and Gauss-Jordan elimination method,the current situation at home and abroad.In the second part,we introduce some symbols and results to be used in this dissertation.In the third part,we introduce specific definitions of the Moore-Penrose inverse,Drazin inverse of the quaternion tensor and the generalized inverse of quaternion tensors with prescribed range S and null space T.Some characterizations,representations and properties of the defined inverses are investigated.Moreover,three algorithms are established for computing the Moore-Penrose inverse,Drazin inverse of the quaternion tensor and the generalized inverse of quaternion tensors with prescribed range S and null space T,respectively.In the fourth part,we first introduce the Gauss-Jordan elimination method.Then based on the above algorithm,the Gauss-Jordan decomposition form and algorithm for computing WG inverse is given,and the algorithm complexity is analyzed.Finally,a numerical example is given.