论文标题
太阳带来的两个身份的概括和替代证明
Generalization and Alternative Proof of Two Identities Posed by Sun
论文作者
论文摘要
我们研究了两种涉及统一根和遗传矩阵的决定因素的身份，这些身份最近通过使用著名的特征矢量 - 元素值身份来证明了正常矩阵。在本文中，我们通过考虑循环矩阵类别将这些身份扩展到更通用的形式。此外，我们为Sun的身份提供了另一种证据，独立于特征向量 - 元素价值身份，在该身份中，我们的策略是建立在与特定矩阵的不必要正常矩阵与具有整数特征值的相似性建立的，该矩阵来自傅立叶变换量。
We study two identities involving roots of unity and determinants of Hermitian matrices which have been recently proved by using the famous eigenvector-eigenvalue identity for normal matrices. In this paper, we extend these identities to a more general form by considering the class of circulant matrices. Furthermore, we give an alternative proof of Sun's identities independent of the eigenvector-eigenvalue identity, where our strategy is built upon the similarity of an unnecessarily normal matrix to a particular matrix with integer eigenvalues, derived from the Fourier transform vectors.
