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

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)

1import numpy as np
2 
3v = np.array([1, 2, 3, 4])
4print("1D Vector shape:", v.shape)        # (4,) -> ndim = 1
5 
6# Convert into a 2D Row Vector (1 row, 4 columns)
7row_vec = v[np.newaxis, :]
8print("Row Vector shape:", row_vec.shape)  # (1, 4) -> ndim = 2
9 
10# Convert into a 2D Column Vector (4 rows, 1 column)
11col_vec = v[:, np.newaxis]
12print("Column Vector shape:
13", col_vec)
14print("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:

1# These two expressions are identical:
2a = np.array([10, 20, 30])
3print(a[np.newaxis, :].shape)  # (1, 3)
4print(a[None, :].shape)        # (1, 3)

Inserting Multiple New Dimensions:

1# Turn a (3,) vector into a (1, 3, 1, 1) 4D tensor
2tensor_4d = a[np.newaxis, :, np.newaxis, np.newaxis]
3print("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:

1x = np.array([[1, 2], [3, 4]])  # shape (2, 2)
2 
3# Insert an axis at position 0: shape becomes (1, 2, 2)
4x_expanded_0 = np.expand_dims(x, axis=0)
5print("axis=0 shape:", x_expanded_0.shape)
6 
7# Insert an axis at position 1: shape becomes (2, 1, 2)
8x_expanded_1 = np.expand_dims(x, axis=1)
9print("axis=1 shape:", x_expanded_1.shape)
10 
11# Insert an axis at the end: shape becomes (2, 2, 1)
12x_expanded_last = np.expand_dims(x, axis=-1)
13print("axis=-1 shape:", x_expanded_last.shape)
14 
15# You can also pass a tuple of axes:
16x_multi = np.expand_dims(x, axis=(0, 3))
17print("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:

1# A tensor with multiple redundant singleton dimensions
2padded_array = np.zeros((1, 28, 28, 1))
3 
4# Squeeze all dimensions of size 1
5squeezed = np.squeeze(padded_array)
6print("Squeezed shape:", squeezed.shape)  # (28, 28)
7 
8# Target specific singleton axes only:
9partially_squeezed = np.squeeze(padded_array, axis=0)
10print("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.

Interactive Quiz• Knowledge Check

Multiple Choice Questions

Question 1

What does np.newaxis evaluate to in Python?

Question 2

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

Question 3

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

Question 4

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

Question 5

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

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Flattening Multi-Dimensional Arrays (flatten vs ravel)	Concatenating & Stacking Arrays (concatenate, vstack, hstack)

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Concatenating & Stacking Arrays (concatenate, vstack, hstack)

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

Beginner12 min read•Updated: Jul 11, 2026

Study Materials Cheatsheet

Expanding & Squeezing Dimensions: np.newaxis & expand_dims

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)

1import numpy as np
2 
3v = np.array([1, 2, 3, 4])
4print("1D Vector shape:", v.shape)        # (4,) -> ndim = 1
5 
6# Convert into a 2D Row Vector (1 row, 4 columns)
7row_vec = v[np.newaxis, :]
8print("Row Vector shape:", row_vec.shape)  # (1, 4) -> ndim = 2
9 
10# Convert into a 2D Column Vector (4 rows, 1 column)
11col_vec = v[:, np.newaxis]
12print("Column Vector shape:
13", col_vec)
14print("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:

1# These two expressions are identical:
2a = np.array([10, 20, 30])
3print(a[np.newaxis, :].shape)  # (1, 3)
4print(a[None, :].shape)        # (1, 3)

Inserting Multiple New Dimensions:

1# Turn a (3,) vector into a (1, 3, 1, 1) 4D tensor
2tensor_4d = a[np.newaxis, :, np.newaxis, np.newaxis]
3print("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:

1x = np.array([[1, 2], [3, 4]])  # shape (2, 2)
2 
3# Insert an axis at position 0: shape becomes (1, 2, 2)
4x_expanded_0 = np.expand_dims(x, axis=0)
5print("axis=0 shape:", x_expanded_0.shape)
6 
7# Insert an axis at position 1: shape becomes (2, 1, 2)
8x_expanded_1 = np.expand_dims(x, axis=1)
9print("axis=1 shape:", x_expanded_1.shape)
10 
11# Insert an axis at the end: shape becomes (2, 2, 1)
12x_expanded_last = np.expand_dims(x, axis=-1)
13print("axis=-1 shape:", x_expanded_last.shape)
14 
15# You can also pass a tuple of axes:
16x_multi = np.expand_dims(x, axis=(0, 3))
17print("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:

1# A tensor with multiple redundant singleton dimensions
2padded_array = np.zeros((1, 28, 28, 1))
3 
4# Squeeze all dimensions of size 1
5squeezed = np.squeeze(padded_array)
6print("Squeezed shape:", squeezed.shape)  # (28, 28)
7 
8# Target specific singleton axes only:
9partially_squeezed = np.squeeze(padded_array, axis=0)
10print("Squeeze axis 0 only:", partially_squeezed.shape)  # (28, 28, 1)

Interactive Quiz• Knowledge Check

Multiple Choice Questions

Question 1

What does np.newaxis evaluate to in Python?

Question 2

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

Question 3

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

Question 4

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

Question 5

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

Next Lesson

Concatenating & Stacking Arrays (concatenate, vstack, hstack)

Continue learning with hands-on practice, examples, and exercises in the upcoming topic.

Related Lessons

Previous Lesson	Next Lesson
Flattening Multi-Dimensional Arrays (flatten vs ravel)	Concatenating & Stacking Arrays (concatenate, vstack, hstack)

Practice Quiz

Test your understanding of this lesson with 5 questions. Each question has one correct answer.

Previous Next

Expanding & Squeezing Dimensions: np.newaxis & expand_dims

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

2. What is np.newaxis?

Inserting Multiple New Dimensions:

3. Explicit Axis Expansion with np.expand_dims()

4. Removing Singleton Dimensions with np.squeeze()

Multiple Choice Questions

Concatenating & Stacking Arrays (concatenate, vstack, hstack)

Related Lessons

Practice Quiz

Loading Page Content...

Expanding & Squeezing Dimensions: np.newaxis & expand_dims

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

2. What is np.newaxis?

Inserting Multiple New Dimensions:

3. Explicit Axis Expansion with np.expand_dims()

4. Removing Singleton Dimensions with np.squeeze()

Multiple Choice Questions

Concatenating & Stacking Arrays (concatenate, vstack, hstack)

Related Lessons

Practice Quiz

2. What is `np.newaxis`?

3. Explicit Axis Expansion with `np.expand_dims()`

4. Removing Singleton Dimensions with `np.squeeze()`

2. What is `np.newaxis`?

3. Explicit Axis Expansion with `np.expand_dims()`

4. Removing Singleton Dimensions with `np.squeeze()`