Linear Algebra 101 -- Part 9: Singular Value Decomposition (SVD)

Singular Value Decomposition (SVD) is another type of decomposition. Unlike eigendecomposition where the matrix you want to decompose has to be a square matrix, SVD allows you to decompose a rectangular matrix (a matrix that has different numbers of rows and columns). This is often more useful in a real-life scenario since the rectangular matrix could represent a wide variety of data that's not a square matrix. First, let's look at the definition itself. As you can see, SVD decomposes the matrix into 3 different matrices.