Numpy matrix operations | identity() function

The numpy.identity() function is a quick and straightforward tool for generating identity matrices. This function complements numpy.eye(), but it's specifically for creating square identity matrices.

1. Introduction:

An identity matrix is a square matrix in which all the elements of the principal (main) diagonal are ones and all other elements are zeros.

2. Basic Setup:

Start by importing the necessary library:

import numpy as np

3. Using `numpy.identity()`:

Creating an Identity Matrix:

To generate a 3x3 identity matrix:

I = np.identity(3)
print(I)

Output:

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

As you can see, it's very direct. You just specify the size of the matrix (number of rows or columns since it's square), and the function does the rest.

Specifying Data Type:

You can also determine the data type of the matrix elements using the dtype parameter:

I_int = np.identity(3, dtype=int)
print(I_int)

Output:

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

4. Differences between `numpy.eye()` and `numpy.identity()`:

While both functions can create identity matrices, there are some differences:

Flexibility: numpy.eye() is more versatile. It can create non-square matrices and matrices with ones on off-diagonals, while numpy.identity() strictly creates square identity matrices.
Simplicity: numpy.identity() is simpler to use when you specifically need a square identity matrix since it requires fewer arguments.

5. Practical Applications:

Matrix Multiplication with Identity:

An identity matrix serves as the "neutral element" in matrix multiplication, analogous to multiplying numbers by 1:

A = np.array([[5, 3], [8, 7]])
result = A @ np.identity(2)
print(result)

Output:

[[5. 3.]
 [8. 7.]]

The product is the matrix A itself, demonstrating the "neutral" property of the identity matrix.

6. Conclusion:

The numpy.identity() function provides a quick and concise way to generate square identity matrices in Python. Given the fundamental nature of identity matrices in linear algebra and numerical computations, having such a function at your disposal is immensely useful. Whether you're working with matrix equations, initializing matrices, or performing other matrix operations, the identity matrix is an indispensable tool.

Numpy matrix operations | identity() function

1. Introduction:

2. Basic Setup:

3. Using numpy.identity():

Creating an Identity Matrix:

Specifying Data Type:

4. Differences between numpy.eye() and numpy.identity():

5. Practical Applications:

Matrix Multiplication with Identity:

6. Conclusion:

3. Using `numpy.identity()`:

4. Differences between `numpy.eye()` and `numpy.identity()`: