We would try to clearly explain the concept of a recommender system.

**What is a Recommender System**

A recommender system is a system that is used to make prediction about what the user preference may be on the items before the user does it.

We are going to briefly discuss the following three topics:

Matrix factorization is aspect of linear algebra which is the factorization of a matrix into two or more matrices such that when multiplied together would give the original matrix

SVD is a method of matrix factorization. It is a generalization of the eigen-decomposition of a positive semi-definite orthonomal matrix to an m x n matrix through an extension of the polar decomposition.

The singular value decomposition of a matrix M of m x n dimension is a factorization given by

where :

is an m x n matrix

is an m x n rectangular diagonal matrix with non-negative real numbers on the diagonal

is an n x n real or complex unitary matrix

PMF does the factorization of a matrix by learning models using maximum a posterior approximation

We are going to briefly discuss the following three topics:

- Matrix Factorization
- Singular value decomposition(SVD)
- Probabilistic Matrix Factorization (PMF)

**1. Matrix Factorization**Matrix factorization is aspect of linear algebra which is the factorization of a matrix into two or more matrices such that when multiplied together would give the original matrix

**2. Singular Value Decomposition(SVD)**SVD is a method of matrix factorization. It is a generalization of the eigen-decomposition of a positive semi-definite orthonomal matrix to an m x n matrix through an extension of the polar decomposition.

The singular value decomposition of a matrix M of m x n dimension is a factorization given by

where :

is an m x n matrix

is an m x n rectangular diagonal matrix with non-negative real numbers on the diagonal

is an n x n real or complex unitary matrix

**3. Probabilistic Matrix Factorization(PMF)**PMF does the factorization of a matrix by learning models using maximum a posterior approximation