NumPy Operations

From a list

np.array([1, 2, 3])

Shape (3,), a 1-D array.

Zeros / ones

np.zeros((2, 3))

Give the shape as a tuple; here (2, 3).

Range

np.arange(6)

[0 1 2 3 4 5], shape (6,).

Random normal

np.random.randn(2, 3)

Standard-normal entries, shape (2, 3).

Inspect shape

x.shape

Tuple of dimension sizes.

Number of dims

x.ndim

Length of x.shape.

Reshape

x.reshape(3, 4)

Total elements must match; use -1 to infer one axis.

Add an axis

x[:, None]

(n,) becomes column (n, 1).

Sum all

x.sum()

Returns a scalar.

Sum over an axis

x.sum(axis=0)

Collapses that axis; (m, n) → (n,).

Mean over an axis

x.mean(axis=1)

(m, n) → (m,); use keepdims=True to keep (m, 1).

Argmax

x.argmax(axis=1)

Index of max along the axis; drops that axis.

Matrix multiply

A @ B

(m, n) @ (n, p) → (m, p).

Transpose

A.T

(m, n) → (n, m).

Vector / matrix norm

np.linalg.norm(x)

L2 by default; pass axis= for row/column norms.

Solve $Ax = b$

np.linalg.solve(A, b)

Prefer over inv(A) @ b: faster and more stable.

Broadcasting

A + b

(m, n) + (n,) adds b to every row; axes align from the right.

Element-wise op

A * B

Equal shapes (or broadcastable); element-wise product.