As a beginner in data science, understanding matrix multiplication is crucial to be able to work with arrays and matrices in Python. In this article, we will cover everything you need to know about matrix multiplication using Python Numpy.
Introduction
In data science, matrix multiplication is a fundamental operation used in a variety of tasks, including linear regression, clustering, and deep learning. Matrix multiplication allows us to combine matrices to perform transformations and operations that would not be possible with individual vectors or scalars. With Python Numpy, matrix multiplication is easy and efficient to perform.
Basic Concepts of Matrix Multiplication
Before we dive into the implementation of matrix multiplication using Python Numpy, let’s first review some basic concepts.
Matrix Dimensions
Matrices are defined by their dimensions, which are represented as (rows, columns). For example, a matrix with three rows and two columns would be represented as a (3,2) matrix.
Scalar Multiplication
Scalar multiplication involves multiplying a matrix by a scalar value. This is done by multiplying each element in the matrix by the scalar value.
Matrix Addition
Matrix addition involves adding two matrices of the same dimensions. This is done by adding each corresponding element in the matrices.
Dot Product
The dot product of two matrices involves multiplying the corresponding elements in each row of the first matrix with the corresponding elements in each column of the second matrix and then summing the products.
Matrix Multiplication
Matrix multiplication is the most complex of these operations. It involves multiplying the rows of the first matrix by the columns of the second matrix to obtain a new matrix.
Implementing Matrix Multiplication with Python Numpy
Python Numpy provides an efficient way to implement matrix multiplication. Let’s see how to do this step by step.
Step 1: Import Numpy
The first step is to import the Numpy library. This is done by typing the following code:
import numpy as np
Step 2: Create Matrices
Next, we need to create the matrices that we want to multiply. For example, let’s create two matrices:
a = np.array([[1,2],[3,4]])
b = np.array([[5,6],[7,8]])
Step 3: Perform Matrix Multiplication
To perform matrix multiplication, we use the dot() function. For example, to multiply the two matrices we just created, we would type the following:
c = np.dot(a,b)
The resulting matrix c would be:
array([[19, 22],
[43, 50]])
Conclusion
In this article, we covered the basics of matrix multiplication and how to implement it using Python Numpy. With this knowledge, you can now perform matrix multiplication in Python to perform a variety of data science tasks.