Matrix Multiplication Calculator

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

-1 2 5 3 4 6 -8 2 12

Matrix A

-2 2 5 7 -1 4

Matrix B

Calculation precision

Digits after the decimal point: 2

Calculate

Result

 

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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 and are defined as:
.

,

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:

- 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.