Dot Product
Table of Content:
Dot Product
Dot Product
-
If A is a
m × n
matrix and B is an n × p matrix, then the dot product of matrix A and matrix B is a m × p matrix, where then
entries across a row of A are multiplied with then
entries down a column of B and summed to generate an entry of resulting matrix. -
The dot product greatly reduces the computation time especially when we have a large number of independent equations to solve.
-
Note that the number of columns in the first matrix should always be equal to the number of rows in the second matrix.
-
We use
dot() function
of NumPy package in python to compute the dot product.
Element-Wise Product
-
There are few situations where you need to compute
element-wise multiplication
of two matrices of same dimensions. -
The resulting dimension will be same as the dimensions of two matrices used for element-wise multiplication.
-
We use
multiply()
function of numpy package in python to compute element-wise product of two matrices.
Dot product Example
Sample code in Python for a dot product
import numpy as np #matrix a a = np.array([[1,2],[3,4]]) print("matrix a dimension ", a.shape) #matrix b b = np.array([[5,6,7],[8,9, 10]]) print("matrix b dimension ", b.shape) #matrix c = a.b c = np.dot(a,b) print("dot product of a and b: ", c) print("matrix c dimension ", c.shape)
Output:
output: matrix a dimension (2, 2) matrix b dimension (2, 3) dot product of a and b: [[21 24 27] [47 54 61]] matrix c dimension (2, 3)