Matrix Multiplication Calculator

Perform matrix multiplication by entering the elements of two matrices. The calculator will compute the product matrix.

Anton

Created: 2011-03-28 13:12:07, Last updated: 2023-05-27 14:14:28

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Using the calculator

Enter the elements of Matrix A and Matrix B in the respective text fields, separating the elements by spaces and new lines. The calculator will compute the matrix product and display the result.

Matrix Multiplication

Digits after the decimal point: 2
Result

Matrix Multiplication

The calculator performs matrix multiplication of two matrices, A and B. The product matrix, C, is obtained by multiplying the corresponding elements of the matrices as follows:
The matrixes $A(m \times n)$ and $B(n \times q)$ are defined as:
$A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix},\;\;\; B = \begin{bmatrix} b_{11} & b_{12} & \cdots & b_{1q} \\ b_{21} & b_{22} & \cdots & b_{2q} \\ \vdots & \vdots & \ddots & \vdots \\ b_{n1} & b_{n2} & \cdots & b_{nq} \end{bmatrix}$.

$C = A \times B = \begin{bmatrix} c_{11} & c_{12} & \cdots & c_{1q} \\ c_{21} & c_{22} & \cdots & c_{2q} \\ \vdots & \vdots & \ddots & \vdots \\ c_{m1} & c_{m2} & \cdots & c_{mq} \end{bmatrix}$,

To compute each element of the product matrix, we take the dot product of the i-th row of matrix A and the j-th column of matrix B. The dot product is obtained by summing the products of corresponding elements:

$c_{i,j} = \sum_{r=1}^n a_{i,r}b_{r,j} \;\;\; \left(i=1, 2, \ldots m;\;j=1, 2, \ldots q \right)$ - the summation is taken over the common dimension (r = 1 to n).

The dimensions of the matrices must satisfy (n × m)(m × p) = (n × p) for matrix multiplication to be defined.

Please note that matrix multiplication is not commutative, except when both matrices are diagonal and have the same dimension.

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PLANETCALC, Matrix Multiplication Calculator