# Vectorization in Python

In this article, we learn about Vectorization in Python.

VECTORIZATION

- Vectorization is a technique of executing operations on entire arrays without using a loop.
- Vectorization helps to speed up the Python code.
- There are various operations are being performed over vector instead of arrays such as Dot Product, Outer Product, Element wise Product.

DOT PRODUCT (INNER PRODUCT)

- The dot product of vectors which is also known as the scalar product as it produces a single output
- The dot product is an algebraic operation in which two equal length vectors are being multiplied and it produces a single number.

**Example:**

- Let’s consider two matrix
*a*and*b*of the same length, the dot product is done by taking the transpose of the first matrix and then mathematical matrix multiplication of*a’*(transpose of a) and*b*is followed as shown in the figure below.

OUTER PRODUCT

- The tensor product of two coordinate vectors is termed as
**Outer Product**. - The outer products which result in a square matrix of dimension equal to (length X length) of the vectors.

**Example:**

- Let’s consider two vectors
*a*and*b*with dimension n x 1 and m x 1 then the outer product of the vector results in a rectangular matrix of n x m. - If two vectors have the same dimension then the resultant matrix will be square as shown in the figure.

ELEMENT WISE PRODUCT

- Element wise multiplication of two matrices is the algebraic operation in which each element of the first matrix is multiplied by its corresponding element in the later matrix.
- The dimension of the matrices should be the same.

**Example:**

- In the below example, consider two matrices
*a*and*b*, index of an element in*a*is*i*and*j*then*a(i, j)*is multiplied with*b(i, j)*respectively as shown in the figure below.

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