الجبر الخطي بـ numpy

import numpy as np

u = np.array([-3, -2, 0, -1, 4])
v = np.array([-1, -1, 2, -3, 5])
print("u · v =", np.dot(u, v))

A = np.array([[1, 2], [3, 4]])
B = np.array([[0, 1], [1, 0]])
print("A @ B =\n", A @ B)
print("B @ A =\n", B @ A)
print("هل الضرب إبدالي؟", np.array_equal(A @ B, B @ A))

import numpy as np

M = np.array([
    [-1, 0, 1],
    [-2, -3, 4],
    [1, 5, 6],
])
v = np.array([1, -3, 2])

print(M @ v)
print("المنقولة:\n", M.T)
print("(AB)ᵀ = BᵀAᵀ ؟",
      np.array_equal((M @ M).T, M.T @ M.T))

import numpy as np

u = np.array([-2, 3])
v = np.array([1, 2, -3])

print("u ⊗ v =", np.kron(u, v))
print("v ⊗ u =", np.kron(v, u))

A = np.array([[1, 2], [3, 4]])
B = np.array([[0, 5], [6, 7]])
T = np.kron(A, B)
print("أبعاد A ⊗ B:", T.shape)
print(T)

import numpy as np

a = np.array([1 + 1j, 2])
print("np.dot  (خطأ شائع):", np.dot(a, a))
print("np.vdot (الصحيح)  :", np.vdot(a, a))
print("مربّع الطول       :", np.linalg.norm(a) ** 2)