How to Create an Eye Matrix in NumPy: Simple Guide

Use numpy.eye(n, M=None, k=0, dtype=float) to create a 2D array with ones on the diagonal and zeros elsewhere. Here, n is the number of rows, M is the number of columns (optional), and k shifts the diagonal. This function returns an identity-like matrix called an eye matrix.

Syntax

The numpy.eye function creates a 2D array with ones on a specified diagonal and zeros elsewhere.

• n: Number of rows in the output matrix.
• M (optional): Number of columns. If not given, it defaults to n.
• k (optional): Index of the diagonal. 0 is the main diagonal, positive values are above, negative below.
• dtype (optional): Data type of the output array, default is float.

python

numpy.eye(n, M=None, k=0, dtype=float)

Example

This example creates a 4x4 eye matrix with ones on the main diagonal and zeros elsewhere.

python

import numpy as np

# Create a 4x4 eye matrix
eye_matrix = np.eye(4)
print(eye_matrix)

Output

[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]]

Common Pitfalls

Common mistakes when using numpy.eye include:

• Not specifying M when you want a non-square matrix, which defaults to a square matrix.
• Misunderstanding the k parameter, which shifts the diagonal. Positive k moves the diagonal up, negative moves it down.
• Forgetting to set dtype if you need integers instead of floats.

python

import numpy as np

# Wrong: expecting a 3x4 matrix but only passing n=3
wrong_eye = np.eye(3)
print(wrong_eye)

# Right: specify M=4 for 3 rows and 4 columns
right_eye = np.eye(3, 4)
print(right_eye)

# Using k to shift diagonal up by 1
shifted_eye = np.eye(4, k=1)
print(shifted_eye)

# Using dtype=int for integer matrix
int_eye = np.eye(3, dtype=int)
print(int_eye)

Output

[[1. 0. 0.]
 [0. 1. 0.]
 [0. 0. 1.]]
[[1. 0. 0. 0.]
 [0. 1. 0. 0.]
 [0. 0. 1. 0.]]
[[0. 1. 0. 0.]
 [0. 0. 1. 0.]
 [0. 0. 0. 1.]
 [0. 0. 0. 0.]]
[[1 0 0]
 [0 1 0]
 [0 0 1]]

Quick Reference

Parameter	Description	Default
n	Number of rows	Required
M	Number of columns	n (square matrix)
k	Diagonal offset (0=main, +up, -down)	0
dtype	Data type of output array	float

Key Takeaways

Use numpy.eye(n) to create an n x n identity matrix with ones on the main diagonal.

Specify M to create a non-square eye matrix with different columns.

Use k to shift the diagonal up or down from the main diagonal.

Set dtype to control the data type, like int or float.

Remember numpy.eye returns a 2D array with ones on the specified diagonal and zeros elsewhere.