关于酉矩阵的若干结果

Some Conclusions about the U-matrix

在矩阵理论中,经常利用矩阵来描述变换。在实空间中正交变换保持度量不变,而正交变换中对应的变换矩阵就是正交矩阵,所以对正交矩阵的研究就显得格外重要。同样道理,想要得到复空间中保持度量不变的线性变换,就应该对正交变换进行推广,将其推广到复数域上,那对应的正交矩阵相应的也推广到复数域——酉矩阵。通过矩阵理论的深入研究,对正交矩阵与酉矩阵进行比较,得到了酉矩阵的若干结果。

Transform is uescribed by matrix in the matrix theory. In the real space , orthogonal transformation keeps metric not changing, and transform matrix in the orthogonal transformation is orthogonal matrix. So it is very important to research transform matrix. Similarly, if we want to get the linear transformation in the complex space which keeps metric not changing, We should generalize orthogonal transformation and its orthogonal transformation in the complex number field. Based on the study of the matrix theory in detail, comparing with the orthogonal matrix and the U-matrix, some conclusions about the U-matrix are obtained.