Matrix Transposition

Introduction

• Matrix Transposition is an operation that converts one matrix into another.
• Each row in the original matrix is used as a column in the transposed matrix.

Notation

• Using a prime: the transpose of matrix A is A'
• Using a T superscript: the tranpose of matrix A is A^T

Example

code (Python)

import numpy as np

a = np.matrix([[3, 6, 2], [5, 1, 10]])
print(a)

transposed = a.transpose()
print(transposed)

Notes

• The order (or dimension) of a matrix is switched when transposing, i.e. a 3x2 matrix creates a 2x3 matrix.