Matrix Multiplication


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Row And Column Vectors Show

Dot product of row and column vectors Show

Matrix Multiplication


  • 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:


Find the result of multiplying the following two matrices:
  1. First we position them to make it easier to see which vectors need to be multiplied:
  2. Then we write the dot product of the corresponding vectors:
  3. 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)