transpose of a matrix is a flipped version of the original matrix, where the rows and columns are switched
Code
import numpy as np
#create a 3x4 matrix
mat = np.array([[1,2,3], [4,5,6], [7,8,9],[10,11,12]) #np.arange(1, 13).reshape(3,-1)
mat.T == np.transpose(mat)Properties
transpose of a scalar is the scalar itself
transpose of a sum equals the sum of individual transpose
Distribute the scalar out of a product
Transpose of a product equals the product of individual transposes, in reverse order
This can be used to prove that the transpose of an inverse matrix is the inverse of its transpose