如何在 Python 中求解转换矩阵？

Question

我有 n 个向量 v_i, 1<=i<=n, and a starting vector v_0. I would like to solve for an nxn transition matrix A, s.t. A^i * v_0 = v_i for all i. What is the easiest way to implement this in python?

Answer 1

如果v_0 ... v_n是线性无关的，那么A = [v_1 .. v_n] * [v_0 ... v_{n-1}]^-1，即

A = np.hstack((v_1, ..., v_n)) @ inv(np.hstack((v_0, ..., v_n_1)))

.

否则无唯一解。