Search for a tool
Matrix Direct Sum

Tool to calculate the direct sums of matrices. The direct sum calculates the sum of N matrices 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, 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!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Matrix Direct Sum tool. Thank you.

# Matrix Direct Sum

## Direct Sum of 2 Matrices

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

## Answers to Questions

### How to add 2 matrices with direct sum?

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.

### 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. 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 !

## Questions / Comments

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Matrix Direct Sum tool. Thank you.

Source : http://www.dcode.fr/matrix-direct-sum
© 2017 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode