How to Multiply Arrays in NumPy: Syntax and Examples

To multiply arrays in NumPy element-wise, use the * operator or numpy.multiply(). For matrix multiplication, use the @ operator or numpy.dot().

Syntax

NumPy provides two main ways to multiply arrays:

• Element-wise multiplication: multiplies each element of one array by the corresponding element of another array of the same shape.
• Matrix multiplication: performs the dot product of two arrays following linear algebra rules.

Here is the syntax for both:

python

import numpy as np

# Element-wise multiplication
result_elementwise = array1 * array2
# or
result_elementwise_func = np.multiply(array1, array2)

# Matrix multiplication
result_matrix = array1 @ array2
# or
result_matrix_func = np.dot(array1, array2)

Example

This example shows element-wise multiplication and matrix multiplication of two arrays.

python

import numpy as np

# Define two 2x2 arrays
array1 = np.array([[1, 2], [3, 4]])
array2 = np.array([[5, 6], [7, 8]])

# Element-wise multiplication
elementwise = array1 * array2

# Matrix multiplication
matrix_mult = array1 @ array2

print("Element-wise multiplication:\n", elementwise)
print("Matrix multiplication:\n", matrix_mult)

Output

Element-wise multiplication:
 [[ 5 12]
 [21 32]]
Matrix multiplication:
 [[19 22]
 [43 50]]

Common Pitfalls

Common mistakes when multiplying arrays in NumPy include:

• Using * when you want matrix multiplication (it does element-wise instead).
• Trying to multiply arrays with incompatible shapes without broadcasting.
• Confusing np.dot() and np.multiply().

Here is an example showing the wrong and right way:

python

import numpy as np

# Define arrays
array1 = np.array([[1, 2], [3, 4]])
array2 = np.array([[5, 6], [7, 8]])

# Wrong: using * for matrix multiplication
wrong = array1 * array2  # This is element-wise, not matrix

# Right: use @ or np.dot for matrix multiplication
right = array1 @ array2

print("Wrong (element-wise):\n", wrong)
print("Right (matrix multiplication):\n", right)

Output

Wrong (element-wise):
 [[ 5 12]
 [21 32]]
Right (matrix multiplication):
 [[19 22]
 [43 50]]

Quick Reference

Summary of NumPy array multiplication methods:

Operation	Operator / Function	Description
Element-wise multiplication	* or np.multiply()	Multiply arrays element by element
Matrix multiplication	@ or np.dot()	Perform linear algebra matrix multiplication
Broadcasting	Supported with *	Automatically expands smaller arrays to match shapes

Key Takeaways

Use * or np.multiply() for element-wise multiplication of arrays.

Use @ or np.dot() for matrix multiplication following linear algebra rules.

Ensure arrays have compatible shapes for the chosen multiplication method to avoid errors.

Do not confuse element-wise multiplication with matrix multiplication; they produce different results.

Broadcasting allows element-wise multiplication of arrays with different but compatible shapes.