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 takenoffset
(optional) - offset of the diagonal from the main diagonaldtype
(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.