Expanding & Squeezing Dimensions (np.newaxis, expand_dims, squeeze)0%
Concatenating & Stacking Arrays (concatenate, vstack, hstack)

Expanding & Squeezing Dimensions (np.newaxis, expand_dims, squeeze)

Beginner12 min read•Updated: Jul 11, 2026
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Expanding & Squeezing Dimensions: np.newaxis & expand_dims

In linear algebra, matrix multiplication, and deep learning libraries (TensorFlow, PyTorch), the dimensionality of an array must frequently be adjusted to satisfy shape requirements. For example, multiplying a 1D vector of length $N$ by a 2D matrix of shape $(N, M)$ requires expanding the 1D vector into a formal 2D column matrix of shape $(N, 1)$ or row matrix of shape $(1, N)$.

NumPy provides intuitive tools to inject or eliminate singleton dimensions (dimensions of size 1):

  • np.newaxis
  • np.expand_dims()
  • np.squeeze()

1. The Distinction Between 1D Vector vs 2D Matrix

A common conceptual hurdle for beginners is distinguishing between:

  • A 1D vector of shape (N,)
  • A 2D row matrix of shape (1, N)
  • A 2D column matrix of shape (N, 1)
Python
import numpy as np
 
v = np.array([1, 2, 3, 4])
print("1D Vector shape:", v.shape) # (4,) -> ndim = 1
 
# Convert into a 2D Row Vector (1 row, 4 columns)
row_vec = v[np.newaxis, :]
print("Row Vector shape:", row_vec.shape) # (1, 4) -> ndim = 2
 
# Convert into a 2D Column Vector (4 rows, 1 column)
col_vec = v[:, np.newaxis]
print("Column Vector shape:
", col_vec)
print("Column Vector shape:", col_vec.shape) # (4, 1) -> ndim = 2

2. What is np.newaxis?

Under the hood, np.newaxis is simply an alias for Python's None. Whenever np.newaxis (or None) is used in an index slice, NumPy inserts a new axis with length 1 at that position:

Python
# These two expressions are identical:
a = np.array([10, 20, 30])
print(a[np.newaxis, :].shape) # (1, 3)
print(a[None, :].shape) # (1, 3)

Inserting Multiple New Dimensions:

Python
# Turn a (3,) vector into a (1, 3, 1, 1) 4D tensor
tensor_4d = a[np.newaxis, :, np.newaxis, np.newaxis]
print("Tensor shape:", tensor_4d.shape) # (1, 3, 1, 1)

3. Explicit Axis Expansion with np.expand_dims()

While np.newaxis is concise, np.expand_dims(arr, axis) provides explicit programmatic control over the target insertion axis:

Python
x = np.array([[1, 2], [3, 4]]) # shape (2, 2)
 
# Insert an axis at position 0: shape becomes (1, 2, 2)
x_expanded_0 = np.expand_dims(x, axis=0)
print("axis=0 shape:", x_expanded_0.shape)
 
# Insert an axis at position 1: shape becomes (2, 1, 2)
x_expanded_1 = np.expand_dims(x, axis=1)
print("axis=1 shape:", x_expanded_1.shape)
 
# Insert an axis at the end: shape becomes (2, 2, 1)
x_expanded_last = np.expand_dims(x, axis=-1)
print("axis=-1 shape:", x_expanded_last.shape)
 
# You can also pass a tuple of axes:
x_multi = np.expand_dims(x, axis=(0, 3))
print("Multiple axes (0, 3) shape:", x_multi.shape) # (1, 2, 2, 1)

4. Removing Singleton Dimensions with np.squeeze()

The inverse of dimension expansion is squeezing. np.squeeze() strips out all dimensions of size 1, collapsing the array back to its minimal dimensional representation:

Python
# A tensor with multiple redundant singleton dimensions
padded_array = np.zeros((1, 28, 28, 1))
 
# Squeeze all dimensions of size 1
squeezed = np.squeeze(padded_array)
print("Squeezed shape:", squeezed.shape) # (28, 28)
 
# Target specific singleton axes only:
partially_squeezed = np.squeeze(padded_array, axis=0)
print("Squeeze axis 0 only:", partially_squeezed.shape) # (28, 28, 1)
If you specify an axis for np.squeeze() that does not have a size of 1 (e.g. np.squeeze(padded_array, axis=1) where dimension size is 28), NumPy raises ValueError: cannot select an axis to squeeze out which has size not equal to one.

Multiple Choice Questions

1. What does np.newaxis evaluate to in Python?

A. An integer 0 B. None C. A slice object slice(None) D. An ellipsis object ... Answer: B Explanation: In NumPy's implementation, np.newaxis is defined as an alias for None. When placed in index brackets, it inserts a new axis of size 1.

2. If arr = np.array([5, 10, 15]), what is the shape of arr[:, np.newaxis]?

A. (1, 3) B. (3, 1) C. (3,) D. (1, 1, 3) Answer: B Explanation: arr has length 3 along axis 0. Placing np.newaxis at axis 1 adds a second dimension of size 1, resulting in shape (3, 1).

3. What is the resulting shape of np.expand_dims(np.zeros((10, 20)), axis=1)?

A. (1, 10, 20) B. (10, 1, 20) C. (10, 20, 1) D. (10, 20) Answer: B Explanation: Specifying axis=1 inserts a new singleton dimension at index 1, shifting the original second dimension (size 20) to index 2, giving shape (10, 1, 20).

4. What does np.squeeze(np.ones((1, 5, 1, 8))) return?

A. An array of shape (5, 8) B. An array of shape (40,) C. An array of shape (1, 40) D. An error because two axes have size 1 Answer: A Explanation: By default, np.squeeze() removes all dimensions whose size is 1. Axes 0 and 2 have size 1, leaving axes of size 5 and 8 with resulting shape (5, 8).

5. What happens if you run np.squeeze(np.zeros((3, 4)), axis=0)?

A. The array is flattened to shape (12,) B. A ValueError is raised because axis 0 has size 3, not 1 C. The first row is deleted D. Axis 0 is replaced by 1 Answer: B Explanation: np.squeeze() can only remove axes that have a size of 1. Attempting to squeeze an axis with size > 1 raises a ValueError.

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