Search for a tool

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

Results

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 Addition' tool, so feel free to write! Thank you!

### How to add 2 matrices?

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

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

The sum of these 2 matrices $M_1 + M_2 = [c_{ij}]$ is a matrix of the same size, ie. $m$ lines and $n$ columns, with : $$\forall i, j : c_{ij} = a_{ij}+b_{ij}$$

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

### How to add 2 matrices in Excel?

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

### How to add 2 matrices of distinct sizes?

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

### How to add a scalar to a matrix?

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.

## Source code

dCode retains ownership of the online "Matrix Addition" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Matrix Addition" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, 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, copy-paste, or API access for "Matrix Addition" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : 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!