NumPy - Matrix Subtraction

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What is Matrix Subtraction?

Matrix subtraction is an operation where two matrices of the same size are subtracted element-wise. In matrix subtraction, each element of one matrix is subtracted by the corresponding element of the other matrix.

Just like matrix addition, for matrix subtraction to be valid, both matrices must have the same dimensions (the same number of rows and columns).

If you have two matrices, say A and B, of the same size, then their difference C is defined as:

C = A - B

Where,

Cij = Aij - Bij

In simple terms, the element in the i^th row and j^th column of matrix C is the result of subtracting the corresponding elements in matrices A and B.

Example of Matrix Subtraction

Consider the following two matrices:

A = [[5, 8], 
     [7, 10]]

B = [[2, 4], 
     [3, 6]]

The difference C = A - B will be calculated as:

C = [[5-2, 8-4], 
     [7-3, 10-6]] 
  = [[3, 4], 
     [4, 4]]

So, the result of subtracting matrix B from matrix A gives us matrix C:

C = [[3, 4], 
     [4, 4]]

Matrix Subtraction in NumPy

In NumPy, matrix subtraction is done using the - operator or using the numpy.subtract() function. NumPy handles matrix operations like subtraction element-wise, which makes mathematical computations fast and easy.

Following are the key points to remember while performing matrix subtraction −

• Matrix Dimensions: For matrix subtraction to be valid, both matrices must have the same dimensions (same number of rows and columns).
• Element-wise Operations: NumPy automatically handles element-wise operations, making it easy to subtract matrices using the - operator or the numpy.subtract() function.
• Flexible Arrays: NumPy arrays are flexible and can handle matrices of different sizes as long as they are compatible in dimensions.

Creating Matrices in NumPy

Before performing matrix subtraction, let us first create two matrices in NumPy using the np.array() function. These matrices should have the same dimensions for subtraction to work as shown below −

import numpy as np

# Creating two 2x2 matrices
A = np.array([[5, 8], [7, 10]])
B = np.array([[2, 4], [3, 6]])

# Print the matrices
print("Matrix A:")
print(A)
print("\nMatrix B:")
print(B)

Following is the output obtained −

Matrix A:
[[ 5  8]
 [ 7 10]]

Matrix B:
[[2 4]
 [3 6]]

Matrix Subtraction Using the - Operator

The simplest way to subtract two matrices in NumPy is by using the - operator. This operator automatically performs element-wise subtraction of the two matrices.

Example

In the following example, we are subtracting two matrices "A" and "B" using the "-" operator −

import numpy as np

# Creating two 2x2 matrices
A = np.array([[5, 8], [7, 10]])
B = np.array([[2, 4], [3, 6]])

# Subtracting two matrices using the - operator
C = A - B

# Print the result
print("Matrix C (A - B):")
print(C)

The output obtained is as shown below −

Matrix C (A - B):
[[3 4]
 [4 4]]

Using the numpy.subtract() Function

Alternatively, you can subtract matrices using the numpy.subtract() function. This function works the same way as the - operator. It takes two matrices (or arrays) as inputs and returns their difference.

Example

In this example, we are subtracting two matrices "A" and "B" using the "numpy.subtract()" function −

import numpy as np

# Creating two 2x2 matrices
A = np.array([[5, 8], [7, 10]])
B = np.array([[2, 4], [3, 6]])

# Subtracting two matrices using numpy.subtract() function
C = np.subtract(A, B)

# Print the result
print("Matrix C (A - B using numpy.subtract()):")
print(C)

We get the output as shown below −

Matrix C (A - B using numpy.subtract()):
[[3 4]
 [4 4]]

Broadcasting in Matrix Subtraction

Matrix subtraction, like matrix addition, also relies on the concept of broadcasting in NumPy. Broadcasting allows NumPy to perform element-wise operations on arrays of different shapes.

However, for matrix subtraction, both matrices must have the same shape. Broadcasting is not applicable here if the matrices don't match in size.

Example

To give you a sense of how broadcasting works (though not directly applicable to matrix subtraction), here's an example of subtracting a scalar from a matrix −

import numpy as np

# Create a 2x2 matrix
A = np.array([[10, 12], [15, 18]])

# Subtract a scalar from the matrix using broadcasting
B = A - 5

# Print the result
print("Matrix A - 5:")
print(B)

The result produced is as follows −

Matrix A - 5:
[[ 5  7]
 [10 13]]

Error Handling in Matrix Subtraction

If you try to subtract matrices with different shapes, NumPy will raise an error. It is important to ensure the matrices have the same dimensions before attempting subtraction.

Example

Following is an example of mismatch dimension in NumPy while performing matrix subtraction −

import numpy as np

# Create two matrices with different shapes
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6, 7]])

# Try to subtract them (this will raise an error)
C = A - B
print(C)

After executing the above code, we get the following output −

Traceback (most recent call last):
  File "/home/cg/root/6734345c5507a/main.py", line 8, in <module>
C = A - B
ValueError: operands could not be broadcast together with shapes (2,2) (1,3) 

Applications of Matrix Subtraction

• Image Processing: In image processing, matrices represent images as pixel values. Matrix subtraction is used to modify images, such as subtracting certain values to enhance or reduce brightness.
• Data Analysis: In data science, matrices are used to represent datasets. Subtracting matrices can be useful for removing unwanted noise or for normalizing datasets.
• Scientific Computing: In physics and engineering, matrix subtraction is often used to calculate differences between matrices representing different variables or states of a system.
• Computer Graphics: In computer graphics, matrix subtraction helps in transformations and adjustments of shapes or objects in 3D space.