论文标题
在左右特征值的存在
On the existence of left and right eigenvalues
论文作者
论文摘要
在本说明中，我们考虑包含复数副本的任意有限维实际代数。事实证明，矩阵具有来自任意有限维真实代数的条目，该代数包含左侧（右）的左侧（分别为右）的左侧（分别）特征值的矩阵。我们主要结果的快速后果是存在矩阵的左右特征值，其中有有限维替代方案的条目，该代数包含副本，例如，例如八元和更一般的矩阵，带有来自真实cayley-dickson代数的条目。
In this note, we consider arbitrary finite-dimensional real algebras containing a copy of complex numbers. It is proved that matrices with entries from an arbitrary finite-dimensional real algebra containing a square root of negative one in its left (resp. right) associate set have left (resp. right) eigenvalues. A quick consequence of our main result is the existence of left and right eigenvalues for matrices with entries from finite-dimensional alternatives algebras containing a copy of complex numbers, e.g., octonions, and more generally matrices with entries from the real Cayley-Dickson algebras.
