Getting the diagonals of a matrix using NumPy

Overview:

The NumPy function diag() returns the main specified diagonal of a matrix.
For square matrices, the line of elements running from the top-left corner of the matrix to the bottom-right corner of the matrix is called the main diagonal of the matrix.
For rectangular matrices the line connecting the elements whose row number is equal to the column number is called the main diagonal.
The main diagonal is also referred to as principal diagonal, leading diagonal, primary diagonal and major diagonal.
The sum of elements of the main diagonal of a square matrix is called the trace of a matrix.
The determinant of a matrix is computed by LU decomposition method. Using LU decomposition method, the lower triangular matrices and upper triangle matrices of a matrix A are obtained and the elements along the main diagonal of both the matrices are multiplied to get the determinant of a matrix.

Main diagonal of a matrix

Example - Get the diagonal of a rectangular matrix:

# Example Python program that returns the main diagonal of a
# rectangular matrix using the numpy.linalg function diag()
import numpy

# Create a rectangular matrix of order 3x4
elems = numpy.arange(-5, 7)
rectMatrix = elems.reshape(3, 4)
print("Rectangular matrix:")
print(rectMatrix)

print("Main diagonal of the rectangular matrix:")
print(numpy.linalg.diagonal(rectMatrix))

Output:

Rectangular matrix:
[[-5 -4 -3 -2]
[-1 0 1 2]
[ 3 4 5 6]]
Main diagonal of the rectangular matrix:
[-5 0 5]