如何在MATLAB中计算交换矩阵

Question

通信矩阵定义为： https://en.wikipedia.org/wiki/Commutation_matrix

假设我有矩阵

A = [1,2,3;4,5,6];

如何在MATLAB中获取交换矩阵？

Answer 1

不确定它是否在“作弊”，但是您可以尝试：

[m, n] = size(A);
I = reshape(1:m*n, [m, n]); % initialize a matrix of indices of size(A)
I = I'; % Transpose it
I = I(:); % vectorize the required indices
Y = eye(m*n); % Initialize an identity matrix
Y = Y(I,:); % Re-arrange the rows of the identity matrix

那么换向矩阵就是Y。