构造所有实Hessenberg酉矩阵的一个简单算法
A Simple Algorithm for Constructing all Real Hessenberg Unitary Matrices
摘要：
次对角线之下为零的酉矩阵（Hessenberg酉矩阵）在分析中有许多用途。该算法给出了一组关于酉矩阵的必要条件，从而得到稀疏的酉矩阵。本文给出了构造所有实Hessenberg酉矩阵的一个算法。由该算法给出的$n\times n$酉矩阵具有$n-1$变量，可以选择这些变量以给出特定应用所需的附加性质。
英文摘要：
Unitary matrices which are zero below the secondary diagonal (Hessenberg unitary matrices) have many uses in analysis. Given a set of needed conditions on a unitary matrix, this algorithm will give the sparsest unitary matrix. We give an algorithm for constructing all real Hessenberg unitary matrices. The $n\times n$ unitary matrices given by the algorithm have $n-1$ variables which can be chosen to give additional properties needed for a particular application.
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。
