How do you multiply matrix in python?
In Python, we can implement a matrix as nested list (list inside a list). Show
We can treat each element as a row of the matrix. For example The first row can be selected as Multiplication of two matrices X and Y is defined only if the number of columns in X is equal to the number of rows Y. If
X is a Source Code: Matrix Multiplication using Nested Loop
Output [114, 160, 60, 27] [74, 97, 73, 14] [119, 157, 112, 23] In this program, we have used nested This technique is simple but computationally expensive as we increase the order of the matrix. For larger matrix operations we recommend optimized software packages like NumPy which is several (in the order of 1000) times faster than the above code. Source Code: Matrix Multiplication Using Nested List Comprehension
The output of this program is the same as above. To understand the
above code we must first know about built-in function We have used nested list comprehension to iterate through each element in the matrix. The code looks complicated and unreadable at first. But once you get the hang of list comprehensions, you will probably not go back to nested loops. In this tutorial, you’ll learn how to multiply two matrices in Python. You’ll start by learning the condition for valid matrix multiplication and write a custom Python function to multiply matrices. Next, you will see how you can achieve the same result using nested list comprehensions. Finally, you’ll proceed to use NumPy and its built-in functions to perform matrix multiplication more efficiently. How to Check if Matrix Multiplication is ValidBefore writing Python code for matrix multiplication, let’s revisit the basics of matrix multiplication.
You’d have likely come across this condition for matrix multiplication before. However, have you ever wondered why this is the case? Well, it’s because of the way matrix multiplication works. Take a look at the image below. In our generic example, matrix A has m rows and n columns. And matrix B has n rows and p columns. What is the Shape of the Product Matrix?
So to get an element at a particular index in the resultant matrix C, you’ll have to compute the dot product of the corresponding row and column in matrices A and B, respectively. Repeating the process above, you’ll get the product matrix C of shape m x p—with m rows and p columns, as shown below. And the dot product or the inner product between two vectors a and b is given by the following equation. Let’s summarize now:
If you take a closer look, n is the number of columns in matrix A, and it’s also the number of rows in matrix B. And this is precisely the reason why you need the number of columns in matrix A to be equal to the number of rows in matrix B. I hope you understand the condition for matrix multiplication to be valid and how to obtain each element in the product matrix. Let’s proceed to write some Python code to multiply two matrices. Write a Custom Python Function to Multiply MatricesAs a first step, let us write a custom function to multiply matrices. This function should do the following:
Step 1: Generate two matrices of integers using NumPy’s
Step 2:
Go ahead and define the function
Parsing the Function DefinitionLet’s proceed to parse the function definition. Declare C as a global variable: By default, all variables inside a Python function have local scope. And you cannot access them from
outside the function. To make the product matrix C accessible from outside, we’ll have to declare it as a global variable. Just add the Check if matrix multiplication is valid: Use the Use nested loops to compute values: To compute the elements of the resultant matrix, we have to loop through the rows of matrix A, and the outer ▶️ Now that we’ve learned how the Python function to multiply matrices works, let’s call the function with the matrices A and B that we generated earlier.
As matrix multiplication between A and B is valid, the function Use Python Nested List Comprehension to Multiply MatricesIn the previous section, you wrote a Python function to multiply matrices. Now, you’ll see how you can use nested list comprehensions to do the same. Here’s the nested list comprehension to multiply matrices. At first, this may look complicated. But we’ll parse the nested list comprehension step by step. Let’s focus on one list comprehension at a time and identify what it does. We’ll use the following general template for list comprehension:
▶️ Check out our guide List Comprehension in Python – with Examples to gain an in-depth understanding.
Nested List Comprehension ExplainedStep 1: Compute a single value in the matrix C Given row i of matrix A and column j of matrix B, the below expression gives the entry at index (i, j) in matrix C.
If Step 2: Build one row in the matrix C Our next goal is to build an entire row. For row 1 in matrix A, you’ve to loop through all columns in matrix B to get one complete row in matrix C. Go back to the list comprehension template.
And here is the first list comprehension.
Step 3: Build all rows and obtain the matrix C Next, you’ll have to populate the product matrix C by computing the rest of the rows. And for this, you’ve to loop through all rows in matrix A. Go back to the list comprehension yet again, and do the following.
And here’s our final nested list comprehension.🎊
It’s time to verify the result! ✔
If you take a closer look, this is equivalent to the nested for loops we had earlier—just that it’s more succinct. You can also do this all the more efficiently using some built-in functions. Let’s learn about them in the next section. Use NumPy matmul() to Multiply Matrices in PythonThe
Notice how this method is simpler than the two methods we learned earlier. In fact, instead of How to Use @ Operator in Python to Multiply MatricesIn Python, It operates on two matrices, and in general, N-dimensional NumPy arrays, and returns the product matrix.
Here’s how you can use it.
Notice that the product matrix C is the same as the one we obtained earlier. Can You Use np.dot() to Multiply Matrices?If you’ve ever come across code that uses
You’ll see that However, as per
NumPy docs, you should use
As NumPy
implicitly broadcasts this dot product operation to all rows and all columns, you get the resultant product matrix. But to keep your code readable and avoid ambiguity, use Conclusion🎯 In this tutorial, you’ve learned the following.
And that wraps up our discussion on matrix multiplication in Python. As a next step, learn how to check if a number is prime in Python. Or solve interesting problems on Python strings. Happy learning!🎉 How do you multiply 2x2 matrices in Python?Step1: input two matrix. Step 2: nested for loops to iterate through each row and each column. Step 3: take one resultant matrix which is initially contains all 0. Then we multiply each row elements of first matrix with each elements of second matrix, then add all multiplied value.
How do you multiply a matrix in NumPy?There are three main ways to perform NumPy matrix multiplication:. dot(array a, array b) : returns the scalar or dot product of two arrays.. matmul(array a, array b) : returns the matrix product of two arrays.. multiply(array a, array b) : returns the element-wise matrix multiplication of two arrays.. Does Python support matrix multiplication?Python syntax currently allows for only a single multiplication operator *, libraries providing array-like objects must decide: either use * for elementwise multiplication, or use * for matrix multiplication. Right now, most numerical code in Python uses syntax like numpy. dot(a, b) or a.
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