Tool to calculate the direct sums of matrices. The direct sum calculates the sum of N matrices of different sizes.

Matrix Direct Sum - dCode

Tag(s) : Matrix

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!

You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? *Contact-me*!

This page is using the new English version of dCode, *please make comments* !

Sponsored ads

Tool to calculate the direct sums of matrices. The direct sum calculates the sum of N matrices of different sizes.

Consider \( M_1=[a_{ij}] \) a matrix of \( m \) lines and \( n \) columns and \( M_2=[b_{ij}] \) a matrix of \( p \) lines and \( q \) columns.

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: $$ \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \oplus \begin{bmatrix} 7 & 8 \\ 9 & 10 \end{bmatrix} = \begin{bmatrix} 1 & 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 & 0 \\ 0 & 0 & 0 & 7 & 8 \\ 0 & 0 & 0 & 9 & 10 \end{bmatrix} $$

The addition by direct sum does not require any calculation, just copy 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.

The direct addition is generalizable to N matrices, but the order matter.

$$ A \oplus B \oplus C = ( A \oplus B ) \oplus C \neq A \oplus ( B \oplus C ) $$

dCode retains ownership of the source code of the script Matrix Direct Sum. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the Matrix Direct Sum script for offline use, for you, your company or association, see you on contact page !

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

Source : http://www.dcode.fr/matrix-direct-sum

© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode