We can use the LA.eig() function in NumPy to calculate the eigenvalues and eigenvectors. If A is an m×p matrix and B is a p×n matrix, the matrix product C= AB (which is an m×n matrix) is defined as: We use ij or aij to denote the element of matrix A at row i and column j. We can think of a matrix A as a transformation that acts on a vector x by multiplication to produce a new vector Ax. To understand SVD we need to first understand the Eigenvalue Decomposition of a matrix. Bold-face capital letters (like A) refer to matrices, and italic lower-case letters (like a) refer to scalars. In this article, bold-face lower-case letters (like a) refer to vectors. Instead of manual calculations, I will use the Python libraries to do the calculations and later give you some examples of using SVD in data science applications. In this article, I will try to explain the mathematical intuition behind SVD and its geometrical meaning. It also has some important applications in data science. It has some interesting algebraic properties and conveys important geometrical and theoretical insights about linear transformations. In linear algebra, the Singular Value Decomposition (SVD) of a matrix is a factorization of that mat rix into three matrices.

Singular matrix