# NumPy trace()

The `numpy.trace()` function is used to return the sum of the diagonals of the matrix.

### Example

``````import numpy as np

# create a 2D matrix
matrix = np.array([[1, 2],
[4, 6]])

# calculate the trace of the matrix
result = np.trace(matrix)

print(result)

# Output: 7``````

## trace() Syntax

The syntax of `trace()` is:

``numpy.trace(matrix, offset=0, dtype=None, out=None)``

## trace() Arguments

The `trace()` method takes the following arguments:

• `matrix` - the input matrix from which the diagonals are taken
• `offset` (optional) - offset of the diagonal from the main diagonal
• `dtype` (optional) - determines the data-type of the returned matrix

## trace() Return Value

The `trace()` method returns the sum of the diagonals of matrix.

## Example 1: Calculate Trace of a Matrix

``````import numpy as np

# create a matrix
matrix1 = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])

# calculate the trace of the matrix and return integer value
result = np.trace(matrix1, dtype=int)

print(result)  ``````

Output

`15`

In the above example, the trace of the matrix is the sum of the elements on the diagonal of matrix1 (i.e., `1 + 5 + 9 = 15`).

## Example 2: Use of offset Argument in trace()

``````import numpy as np

# create a matrix
matrix1 = np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])

# calculate trace of the matrix with offset 1
result1 = np.trace(matrix1, offset=1)
print("With offset=1:", result1)  # Output: 8 (2 + 6)

# calculate trace of the matrix with offset -1
result2 = np.trace(matrix1, offset=-1)
print("With offset=-1:", result2) # Output: 12 (4 + 8)``````

Output

```With offset=1: 8
With offset=-1: 12```

Here,

• If you set the offset to a positive integer, the function will compute the sum of a diagonal above the main diagonal.
• If you set the offset to a negative integer, the function will compute the sum of a diagonal below the main diagonal.