This paper is an extension of Ref. [1]. Here we study the properties of double determi-nant over quaternion field. The necessary and sufficient existence condition of inverse matrixand its direct expression have been ...This paper is an extension of Ref. [1]. Here we study the properties of double determi-nant over quaternion field. The necessary and sufficient existence condition of inverse matrixand its direct expression have been obtained and the Hadamard theorem has been extendedto the quaternion field.展开更多
Using the quaternion multiplication and the double determinant theory over the quaternion field, we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its princ...Using the quaternion multiplication and the double determinant theory over the quaternion field, we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its principal characteristic values.展开更多
文摘This paper is an extension of Ref. [1]. Here we study the properties of double determi-nant over quaternion field. The necessary and sufficient existence condition of inverse matrixand its direct expression have been obtained and the Hadamard theorem has been extendedto the quaternion field.
文摘Using the quaternion multiplication and the double determinant theory over the quaternion field, we proved that an arbitrary quaternion square matrix is similar to a unique Jordan canonical form indicated by its principal characteristic values.
