么正元素於複化 Jordan 代數及擴充二階錐上之研究

The concept of unitary elements play an important role in a complex vector space; for instance, unitary matrices are powerful tool on algorithm in numerical matrix analysis and computing eigenvalues. However, the characterization of unitary elements in a real vector space is not observable. In this project, we consider the complexification of a Euclidean Jordan algebra equipped with the inner product induced by the inner product in its real form. The Jordan product on a Euclidean Jordan algebra gives a bilinear map on a real vector space, we extend the bilinear map to study unitary concept and its applications.