It is not possible to remember the canonical way to do this (possibly avoiding transference), but this should work:
import numpy as np
M = np.random.random_sample((3, 3))
rgb = np.random.random_sample((5, 4, 3))
slow_result = np.zeros_like(rgb)
for i in range(rgb.shape[0]):
for j in range(rgb.shape[1]):
slow_result[i, j, :] = np.dot(M, rgb[i, j, :])
rgb_reshaped = rgb.reshape((rgb.shape[0] * rgb.shape[1], rgb.shape[2]))
result = np.dot(M, rgb_reshaped.T).T.reshape(rgb.shape)
print np.allclose(slow_result, result)
, Scikit Image: