Search for a tool
Transpose of a Matrix

Tool to compute the transpose of a matrix. The transpose of a matrix M of size mxn is a matrix denoted tM of size nxm created by swapping lines and columns.

Results

Transpose of a Matrix -

Tag(s) : Matrix

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Transpose of a Matrix tool. Thank you.

# Transpose of a Matrix

## Matrix Transpose Calculator NxN

Tool to compute the transpose of a matrix. The transpose of a matrix M of size mxn is a matrix denoted tM of size nxm created by swapping lines and columns.

## Answers to Questions

### How to calculate the transpose of a matrix?

The transposition of a matrix (or transpose of matrix) is one of the simplest matrix operations to perform. On has to invert lines and columns:

$$\text{ If } M = \begin{bmatrix} a & c & e \\ b & d & f \end{bmatrix} \text{ Then } M^T = \begin{bmatrix} a & b \\ c & d \\ e & f \end{bmatrix}$$

The lines are read from left to right and are transposed from top to bottom.

Example: $$M = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \Rightarrow M^t = \begin{bmatrix} 1 & 3 \\ 2 & 4 \end{bmatrix}$$

The transposition of a matrix $$M$$ is noted $$M^t$$ or $$^tM$$. The transposition operation is then noted with an exponent T or t (uppercase or lowercase) prefixed or postfixed.

The transposition is valid on both square matrices and rectangular matrices. A transposed row vector is a column vector and vice versa.

### What is a double transposition?

Transposing twice a matrix returns it unchanged.

The double transposition is the name given to a cryptographic cipher.

## Source code

dCode retains ownership of the source code of the script Transpose of a Matrix online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be given for free. So if you need to download the online Transpose of a Matrix script for offline use, check contact page !

## Questions / Comments

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Transpose of a Matrix tool. Thank you.

Source : https://www.dcode.fr/matrix-transpose
© 2018 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode