Tool to calculate matrix additions in computer algebra. The sum of N matrices is generally obtained by summing the elements of each matrix.

Matrix Addition - 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*!

The addition of 2 matrices is noted $ M_1 + M_2 $ with $ M_1=[a_{ij}] $ ($ m $ rows and $ n $ columns, with $ m = n $ for a square matrix) and $ M_2=[b_{ij}] $ (of the same size: $ m $ rows and $ n $ columns).

The sum of these two matrices $ M_1 + M_2 = [c_{ij}] $ is a matrix of the same size, ie. $ m $ rows and $ n $ columns, with: $$ \forall i, j \quad c_{ij} = a_{ij}+b_{ij} $$

Important rule: The addition of matrices (matrix A *plus* matrix B) can only be done with 2 matrices of the same shape/size/dimension (2x2, 2x3, 3x2, 3x3, etc.).

The addition of matrix is done entry by entry

__Example:__ $$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix} + \begin{bmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{bmatrix} = \begin{bmatrix} 1+7 & 2+8 \\ 3+9 & 4+10 \\ 5+11 & 6+12 \end{bmatrix} = \begin{bmatrix} 8 & 10 \\ 12 & 14 \\ 16 & 18 \end{bmatrix} $$

For all matrices A and B of the same size, A+B = B+A.

A matrix addition in Excel can be achieved by adding the elements with identical coordinates in each matrix.

The addition operation (or sum) for matrices can only be done with same size matrices (all dimensions possible, provided they are exactly the same: 3x4, 4x3, 4x4, 5x5, etc.). Nevertheless, there is the direct sum operation, which can be used with distinct size matrices.

The operation of adding a scalar number to a matrix $ [A] + b $ is not defined, but sometimes it implies the operation $ [A] + [I] b $ with $ I $ the identity matrix of size compatible with A.

dCode retains ownership of the "Matrix Addition" source code. Except explicit open source licence (indicated Creative Commons / free), the "Matrix Addition" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Matrix Addition" 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 Addition" 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 Addition" 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 Addition* on dCode.fr [online website], retrieved on 2024-05-27,

addition,sum,plus,matrix,2x2,2x3,3x2,3x3,3x4,4x3,4x4,5x5

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

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

Feedback