Brouwer定理的一个应用

An appliance of Brouwer's theorem

利用Brouwer不动点定理证明了Perron-Wielandt定理,即正矩阵必有正特征值及方阵的行(列)元素之和为非零常数b时有特征值b.

Using Brouwer's fixed point theorem,proved that any positive matrix has a positive eigenvalue and any n×n matrix A with the sum of each row entries is constant b has b as a eigenvalue.