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Matrix Multiplication is a tool that allows you to easily find the "matrix multiplication (matrix product)" of a specified matrix. With this tool, you can simply enter the numbers for the matrix you want to find the matrix multiplication of, and the calculation result of the matrix multiplication will be automatically displayed.

Results of matrix multiplication

How to use

  1. Enter values ​​in the "Matrix" for A and B.
  2. The "Matrix multiplication (matrix product)" will be calculated automatically.

What is matrix multiplication?

Matrix multiplication is an operation in linear algebra that multiplies two matrices to obtain a new matrix. This calculation plays an important role in many areas of data transformation and numerical computation.

How to calculate matrix multiplication

To multiply matrices A and B, the number of columns in A must match the number of rows in B. The resulting matrix C has size m × p.

The elements of the result matrix Ci,j are calculated as follows:

Ci,j = Σk=1n Ai,k × Bk,j

Calculation example

Consider the following matrices A and B:

1
2
3
4
5
6
×
7
8
9
10
11
12

The resulting matrix C is:

58
64
139
154

Calculation procedure

For C1,1:

For C1,1:

For C1,2:

For C1,2:

For C1,2:

For C2,1:

For C2,1:

C2,1 = (4 × 7) + (5 × 9) + (6 × 11) = 139

For C2,2:

C2,2 = (4 × 8) + (5 × 10) + (6 × 12) = 154

Notes

This tool is available for free.

※This program is created and confirm the operation in PHP8.1.22.
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