How to Find Trace of Matrix Using NumPy

To find the trace of a matrix in NumPy, use the numpy.trace() function which sums the diagonal elements of the matrix. Pass your 2D array to numpy.trace() to get the trace value.

Syntax

The syntax for finding the trace of a matrix using NumPy is:

• numpy.trace(a, offset=0, axis1=-2, axis2=-1, dtype=None, out=None)

Here:

• a is the input array (matrix).
• offset shifts which diagonal to sum (0 is main diagonal).
• axis1 and axis2 specify the axes to consider as the matrix dimensions.
• dtype sets the data type for the output.
• out is an optional output array to store the result.

python

numpy.trace(a, offset=0, axis1=-2, axis2=-1, dtype=None, out=None)

Example

This example shows how to create a 3x3 matrix and find its trace using numpy.trace(). The trace is the sum of the diagonal elements.

python

import numpy as np

matrix = np.array([[1, 2, 3],
                   [4, 5, 6],
                   [7, 8, 9]])

trace_value = np.trace(matrix)
print(trace_value)

Output

15

Common Pitfalls

Common mistakes when finding the trace include:

• Passing a 1D array instead of a 2D matrix, which will cause unexpected results.
• Forgetting that offset changes which diagonal is summed (e.g., offset=1 sums the diagonal above the main diagonal).
• Using non-square matrices without understanding that trace sums the diagonal elements present, which may be fewer than rows or columns.

python

import numpy as np

# Wrong: 1D array
arr_1d = np.array([1, 2, 3])
print(np.trace(arr_1d))  # Output is sum of elements, not a matrix trace

# Right: 2D array
arr_2d = np.array([[1, 2, 3], [4, 5, 6]])
print(np.trace(arr_2d))  # Sums diagonal elements (1 + 5)

Output

6
6

Quick Reference

Summary tips for using numpy.trace():

• Use a 2D NumPy array as input.
• Default offset=0 sums the main diagonal.
• Use offset to sum diagonals above or below the main diagonal.
• Works with non-square matrices by summing the overlapping diagonal elements.

Key Takeaways

Use numpy.trace() to sum the diagonal elements of a matrix easily.

Pass a 2D NumPy array to get the correct trace value.

The offset parameter lets you choose which diagonal to sum.

Trace works on non-square matrices by summing the available diagonal elements.

Avoid passing 1D arrays to numpy.trace() as it may give unexpected results.