Introduction
- Matrix Multiplication, or matrix product, is a method of multiplying two matrices to produce a third matrix.
- Two matrices can only be multiplied together if the number of rows in the first matrix is equal to the number of columns in the second matrix.
- The result will be a matrix with the number of columns from the first matrix and the number of rows from the second matrix.
- A is a i x j matrix
- B is a j x k matrix
- C = AB
- C is a i x k matrix
- The values in the resulting matrix are calculated by finding the dot product, using the row from the first matrix and the column from the second:
Example
Find the result of multiplying the following two matrices:Solution
- First we position them to make it easier to see which vectors need to be multiplied:
- Then we write the dot product of the corresponding vectors:
- And finally solve:
code (Python)
import numpy as np
a = [[1, 4], [3, 7], [8, 4]]
b = [[3, 6, 2], [5, 1, 10]]
c = np.matmul(a, b)
print(c)