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.

Matrix Subtraction - dCode

Tag(s) : Matrix

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*!

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 : $$ \forall i, j : c_{ij} = a_{ij}-b_{ij} $$

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

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.

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, breaker, 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, mobile, tablet, iPhone or Android app!

Reminder : dCode is free to use.

The copy-paste of the page "Matrix Subtraction" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!

Exporting results as a .csv or .txt file is free by clicking on the *export* icon

Cite as source (bibliography):

*Matrix Subtraction* on dCode.fr [online website], retrieved on 2024-06-15,

subtraction,minus,matrix,2x2,3x3

https://www.dcode.fr/matrix-subtraction

© 2024 dCode — El 'kit de herramientas' definitivo para resolver todos los juegos/acertijos/geocaching/CTF.

Feedback