How to create an identity matrix using Numpy?

An identity matrix is a square matrix where diagonal elements are 1 and all other elements are 0. NumPy provides the identity() function to create identity matrices efficiently.

Syntax

numpy.identity(n, dtype=None)

Parameters

n: Size of the identity matrix (n x n)
dtype: Data type of the matrix elements (optional, defaults to float)

Creating a Basic Identity Matrix

import numpy as np

# Create a 3x3 identity matrix
identity_matrix = np.identity(3)
print(identity_matrix)

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

Specifying Data Type

import numpy as np

# Create a 4x4 identity matrix with integer type
identity_matrix = np.identity(4, dtype=int)
print(identity_matrix)

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

Using Different Data Types

import numpy as np

# Complex number identity matrix
complex_identity = np.identity(2, dtype=complex)
print("Complex identity matrix:")
print(complex_identity)

# Boolean identity matrix
bool_identity = np.identity(3, dtype=bool)
print("\nBoolean identity matrix:")
print(bool_identity)

Complex identity matrix:
[[1.+0.j 0.+0.j]
 [0.+0.j 1.+0.j]]

Boolean identity matrix:
[[ True False False]
 [False  True False]
 [False False  True]]

Alternative: Using eye() Function

import numpy as np

# Using np.eye() for identity matrix
eye_matrix = np.eye(3, dtype=int)
print("Using np.eye():")
print(eye_matrix)

# np.eye() can also create rectangular matrices
rectangular = np.eye(3, 4, dtype=int)
print("\nRectangular matrix with np.eye():")
print(rectangular)

Using np.eye():
[[1 0 0]
 [0 1 0]
 [0 0 1]]

Rectangular matrix with np.eye():
[[1 0 0 0]
 [0 1 0 0]
 [0 0 1 0]]

Comparison

Conclusion

Use np.identity() to create square identity matrices with specified data types. For more flexibility, including rectangular matrices, use np.eye() instead.