Search for a tool
Matrix Subtraction

Tool to calculate matrix subtraction in algebra. The matrix subtraction is similar to the addition, it is obtained by subtracting the elements of each matrix.

Results

Matrix Subtraction -

Tag(s) : Matrix

Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Thanks to your feedback and relevant comments, dCode has developed the best 'Matrix Subtraction' tool, so feel free to write! Thank you!

Matrix Subtraction

Subtraction of 2 Matrices

What is a matrix subtraction? (Definition)

Take 2 matrices of identical size: $M_1=[a_{ij}]$ a matrix of $m$ rows and $n$ columns (with $m = n$ in the case of a square matrix) and $M_2=[b_{ij}]$ another matrix of $m$ lines and $n$ columns.

The subtraction of these 2 matrices $M_1 - M_2 = [c_{ij}]$ is an unchanged size matrix with $m$ lines and $n$ columns, such as : $$\forall i, j : c_{ij} = a_{ij}-b_{ij}$$

How to subtract 2 matrices?

Subtracting matrices is only defined with 2 matrices of the same shape (square 2x2, 3x3 or rectangular 2x3, 3x2, etc.). The calculation consists in subtracting the elements in the same position in each matrix.

Example: $$\begin{bmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{bmatrix} - \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} = \begin{bmatrix} 7-1 & 8-2 \\ 9-3 & 10-4 \\ 11-5 & 12-6 \end{bmatrix} = \begin{bmatrix} 6 & 6 \\ 6 & 6 \\ 6 & 6 \end{bmatrix}$$

How to subtract 2 matrices of distinct sizes?

The marix subtraction operation is only defined with identical shapes matrices (as the operation of matrix addition). Another operation called direct sum allows the use of matrices of different sizes and can be generalized to subtraction.

Source code

dCode retains ownership of the "Matrix Subtraction" source code. Except explicit open source licence (indicated Creative Commons / free), the "Matrix Subtraction" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Matrix Subtraction" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Matrix Subtraction" are not public, same for offline use on PC, tablet, iPhone or Android !
The copy-paste of the page "Matrix Subtraction" or any of its results, is allowed as long as you cite the online source https://www.dcode.fr/matrix-subtraction
Reminder : dCode is free to use.

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Thanks to your feedback and relevant comments, dCode has developed the best 'Matrix Subtraction' tool, so feel free to write! Thank you!

Source : https://www.dcode.fr/matrix-subtraction
© 2022 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback