In either case, we seek to understand the covariance structure in multivariate data. PCA is used in two broad areas: a.) as a remedy for multicollinearity and b.) as a dimension reduction tool. Principal Component Analysis is the process of computing principal components and use those components in understanding data. In linear algebra, PCA is a rotation of the coordinate system to the canonical coordinate system, and in numerical linear algebra, it means a reduced rank matrix approximation that is used for dimension reduction. In statistics, PCA is the transformation of a set of correlated random variables to a set of uncorrelated random variables. Principal Components Analysis (PCA) may mean slightly different things depending on whether we operate within the realm of statistics, linear algebra or numerical linear algebra.
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