@ symbol in python matrix

@ symbol in python matrix

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In Python, the @ symbol is used for matrix multiplication. When you use @, Python will perform element-wise multiplication on two matrices and return a new matrix.

Here's an example:

import numpy as np
Create two 3x3 matrices
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
B = np.array([[10, 11, 12], [13, 14, 15], [16, 17, 18]])
Multiply two matrices using the @ symbol
C = A @ B
print(C)

This code will output:

[[58 64 70]
[139 154 169]
[220 236 252]]

As you can see, the @ symbol is used to perform matrix multiplication between A and B, resulting in a new matrix C.

Now, let's talk about why we use @ for matrix multiplication. In Python, the @ symbol is often referred to as the "matrix multiplication operator". When you multiply two matrices using the @ symbol, Python will perform element-wise multiplication on each pair of corresponding elements in the input matrices.

In more technical terms, when you multiply two matrices A and B using @, Python performs a dot product between each row of A and each column of B. This is equivalent to summing the products of corresponding elements from each row of A and each column of B.

Here's the math behind it:

C = A @ B = (a11*b10 + a12*b11 + ... + a13*b14) ... (a31*b30 + a32*b31 + ... + a33*b34)

Where A and B are matrices, and a and b are elements of those matrices.

In summary, the @ symbol in Python is used for matrix multiplication. When you multiply two matrices using @, Python performs element-wise multiplication on each pair of corresponding elements in the input matrices. This results in a new matrix that represents the dot product between each row of the first matrix and each column of the second matrix.

I hope this explanation helps clarify how the @ symbol works for matrix multiplication!

What are the symbols in Python?

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