Let Q be the real quaternion field.Let the set of all matrices A=(α<sub>ij</sub>)<sub>n×m</sub>be Q<sub>n×m</sub>where α<sub>ij</sub>∈Q,A<sup>+</su...Let Q be the real quaternion field.Let the set of all matrices A=(α<sub>ij</sub>)<sub>n×m</sub>be Q<sub>n×m</sub>where α<sub>ij</sub>∈Q,A<sup>+</sup> be the conjugate transpose of A.Over a long period of time,there have been various kinds of definitions of determinantover the real quaternion field,but all of them are not concerning the entries of thematrix directly,that is"undirectly".From the point of view how the theory of determi-nant is algebraically developed for skew field,it may be worthwhile defined展开更多
文摘Let Q be the real quaternion field.Let the set of all matrices A=(α<sub>ij</sub>)<sub>n×m</sub>be Q<sub>n×m</sub>where α<sub>ij</sub>∈Q,A<sup>+</sup> be the conjugate transpose of A.Over a long period of time,there have been various kinds of definitions of determinantover the real quaternion field,but all of them are not concerning the entries of thematrix directly,that is"undirectly".From the point of view how the theory of determi-nant is algebraically developed for skew field,it may be worthwhile defined
