Search for a tool
Matrix Direct Sum

Tool to calculate the direct sums of matrices (formal computation). The matricial direct sum calculates the sum of N matrices that can be of different sizes.

Results

Matrix Direct Sum -

Tag(s) : Matrix

dCode and you

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!


Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Matrix Direct Sum tool. Thank you.

  >  [News]: Discover the next version of dCode Matrix Direct Sum!

Matrix Direct Sum

Sponsored ads

Direct Sum of 2 Matrices



Tool to calculate the direct sums of matrices (formal computation). The matricial direct sum calculates the sum of N matrices that can be of different sizes.

Answers to Questions

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

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

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 source code of the script Matrix Direct Sum online. 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, Matlab, etc.) which dCode owns rights will not be given for free. To download the online Matrix Direct Sum script for offline use on PC, iPhone or Android, ask for price quote on contact page !

Questions / Comments

  >  [News]: Discover the next version of dCode Matrix Direct Sum!


Team dCode likes feedback and relevant comments; to get an answer give an email (not published). It is thanks to you that dCode has the best Matrix Direct Sum tool. Thank you.


Source : https://www.dcode.fr/matrix-direct-sum
© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode
Feedback