Matrix decomposition is also called matrix factorisation. Unfortunately, many matrix operations cannot be solved efficiently. However, in the same way, that integers can be decomposed into prime factors to make calculations simpler, and we can use matrix decomposition to reduce a matrix into parts that make it easier to calculate more complex matrix operations. Such parts are, for instance, diagonal matrices and triangular matrices (which only have values in the main diagonal and either the top right half or bottom left half of the matrix). There are many types of matrix decomposition, and in this chapter, you will learn two different matrix decomposition methods: eigendecomposition and singular value decomposition. In addition, you will learn an application of eigendecomposition—principal component analysis.