This paper will explain Principal Components Analysis, where “respecting structure” means “preserving variance”. Explain how to do PCA, show an example, and describe some of the issues that come up in interpreting the results. PCA has been rediscovered many times in many fields, so it is also known as the Karhunen-Loeve transformation, the Hotelling transformation, the method of empirical orthogonal functions, and singular value decomposition. We will call it PCA. Principal Components: Mathematics, Example, Interpretation