Linear transformations on that preserve the Ky Fan k-norm and a remarkable special case when (n k) = (4, 2)
Linear transformations on that preserve the Ky Fan k-norm and a remarkable special case when (n k) = (4, 2)
复制标题
线性变换保留了 Ky Fan k 范数以及 (n k) = (4, 2) 时的显着特例
DOI：
--
复制
发表时间：
1988
期刊：
影响因子：
--
通讯作者：
Chi
中科院分区：
文献类型：
--
作者：
Charles R. Johnson;T. Laffey;Chi
给定一个n×n实矩阵A，它的Ky Fan k范数定义为它的k个最大奇异值之和。我们确定了保持Ky Fan k-范数的线性变换T的结构。我们证明了除(n，k)=(4，2)外，还存在正交阵U和V，其中A+表示A或表示A。对于特殊情况，(n，k)=(4，2)T是上面提到的通常形式，或者等价于通常形式与具有许多显著性质的特定算子的组合。
Given an n × n real matrix A. the Ky Fan k-norm of it is defined as the sum of its k largest singular values. We determine the structures of the linear transformations T on that preserve the Ky Fan k-norm. We show that except for (n,k) = (4,2), there exist orthogonal matrices U and V such that where A+ either denotes A or denotes At . For the particular case (n,k) = (4, 2)T is either of the usual form mentioned above or equivalent to the composition of the usual form with a particular operator that has many remarkable properties.