# matrix transpose

(1.4 hours to learn)

## Summary

The matrix transpose is an operator which flips a matrix over its diagonal, i.e. it switches the row and column indices of the matrix.

## Context

This concept has the prerequisites:

- matrix multiplication (The transpose of a product is the product of transposes, reversed.)

## Core resources (read/watch one of the following)

## -Free-

→ Khan Academy: Linear Algebra

- Lecture "Transpose of a matrix"
- Lecture "Transpose of a matrix product"
- Lecture "Transposes of sums and inverses"
- Lecture "Transpose of a vector"

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 2.7, up to "Permutation matrices," pages 107-110

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

## -Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 1.4.2, "The transpose," pages 36-38

## See also

-No Additional Notes-