Tool to calculate matrix products. Matrix product algebra consists of the multiplication of matrices (square or rectangular).

Matrix Product - 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*!

Tool to calculate matrix products. Matrix product algebra consists of the multiplication of matrices (square or rectangular).

$ M_1=[a_{ij}] $ is a matrix of $ m $ lines and $ n $ columns and $ M_2=[b_{ij}] $ is a matrix of $ n $ lines and $ p $ columns (2x2,2x3,3x2,3x3,etc.). The **matrix product** $ M_1.M_2 = [c_{ij}] $ is a matrix of $ m $ lines and $ p $ columns, with: $$ \forall i, j : c_{ij} = \sum_{k=1}^n a_{ik}b_{kj} $$

__Example:__ $$ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \cdot \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} = \begin{bmatrix} 1 \times 1 + 2 \times 0 & 1 \times 0 + 2 \times 1 \\ 3 \times 1 + 4 \times 0 & 3 \times 0 + 4 \times 1 \end{bmatrix} = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} $$

The order of the operands matters with matrix computations, so $$ M_1.M_2 \neq M_2.M_1 $$

The product of the matrix $ M=[a_{ij}] $ by a scalar (number) $ \lambda $ is a matrix of the same size than the initial matrix $ M $, with each items of the matrix multiplied by $ \lambda $.

$$ \lambda M = [ \lambda a_{ij} ] $$

Associativity : $$ A \times (B \times C) = (A \times B) \times C $$

Distributivity : $$ A \times (B + C) = A \times B + A \times C $$

$$ (A + B) \times C = A \times C + B \times C $$

$$ \lambda (A \times B) = (\lambda A) \times B = A \times (\lambda B) $$

There is a **matrix product** compatible with any matrix sizes: the Kronecker product.

dCode retains ownership of the source code of the script Matrix Product 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 released for free. To download the online Matrix Product script for offline use on PC, iPhone or Android, ask for price quote on contact page !

product,multiplication,matrix,scalar,number,2x2,2x3,3x2,3x3,3x4,4x3,4x4,5x5

Source : https://www.dcode.fr/matrix-multiplication

© 2020 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.

Feedback

▲