Tool to calculate the direct sums of matrices (formal computation). The matrix direct sum calculates the sum of N matrices that can be of different sizes.
Matrix Direct Sum - 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!
Matrix Direct Sum
Sponsored adsDirect Sum of 2 Matrices
Answers to Questions (FAQ)
How to add 2 matrices with direct sum?
Given $ M_1=[a_{ij}] $ a matrix of $ m $ lines and $ n $ columns and $ M_2=[b_{ij}] $ a matrix of $ p $ lines and $ q $ columns (2x2, 2x3, 3x2, 3x3, etc).
The direct sum of these 2 matrices is noted with the character ⊕ (circled plus sign) $ M_1 \oplus M_2 $ and is a matrix of $ m+p $ lines and $ n+q $ columns.
$$ A \oplus B = \begin{bmatrix} [a_{ij}] & [0] \\ [0] & [b_{ij}] \end{bmatrix} $$
Example: $$ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \oplus \begin{bmatrix} 7 & 8 \\ 9 & 10 \end{bmatrix} = \begin{bmatrix} 1 & 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 & 0 \\ 0 & 0 & 0 & 7 & 8 \\ 0 & 0 & 0 & 9 & 10 \end{bmatrix} $$
Practically, the matrix addition by direct sum does not require any calculation, it only consist in copying the matrices diagonally, into a larger one, and fill with zeros.
The direct sum operation must be distinguished from the conventional operation of matrix addition, although it may take different size matrices, the result is not at all identical.
How to add N matrices with direct sum?
The direct addition is generalizable to N matrices, but the order matter.
$$ A \oplus B \oplus C = ( A \oplus B ) \oplus C \neq A \oplus ( B \oplus C ) $$
Source code
dCode retains ownership of the online "Matrix Direct Sum" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Matrix Direct Sum" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Matrix Direct Sum" 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 Direct Sum" 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!
Questions / Comments
Thanks to your feedback and relevant comments, dCode has developed the best 'Matrix Direct Sum' tool, so feel free to write! Thank you!