arXiv 2203.159192022-03math.RA

关于左右特征值的存在性

On the existence of left and right eigenvalues

Bamdad R. Yahaghi

备注：: Unfortunately, the main result of the note, namely Theorem 2.1 is false. Any scalar matrix with a quaternion or octonion that is not a complex number on its main diagonal cannot have left eigenvalues in complex numbers. At this point, I would like to thank Professor Alberto Elduque and an anonymous reviewer of the note for pointing out diagonal matrix counterexamples to me

摘要：

本文考虑了任意有限维实代数中含有一个复数拷贝。证明了任意有限维实代数的元素在其左（或左）方含有一个负1的平方根的矩阵，其左（或右）方含有一个负1的平方根。右）相关联的集合具有左（分别）。右）特征值。我们的主要结果的一个快速的结果是存在的左和右特征值的矩阵的条目从有限维替代代数包含一个副本的复数，例如，八元数，以及更一般地，具有来自实Cayley-Dickson代数的条目的矩阵。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文