Tool to calculate matrix product algebra. The matrix product consists of the multiplication of matrices.

Matrix Product - 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*!

Sponsored ads

Tool to calculate matrix product algebra. The matrix product consists of the multiplication of matrices.

Consider \( M_1=[a_{ij}] \) a matrix of \( m \) lines and \( n \) columns and \( M_2=[b_{ij}] \) a matrix of \( n \) lines and \( p \) columns. 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 \( \lambda \) 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, etc.) which dCode owns rights can be transferred after sales quote. So if you need to download the online Matrix Product script for offline use, for you, your company or association, see you on contact page !

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

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

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