Most generally described as an ordination technique for describing the variation in a multivariate data set. The first axis (the first principal component, or PC) describes the maximum variation in the whole data set, the second describes the maximum variation remaining, and so forth, with each axis orthogonal to the preceding axis. (Allaby, 1994) (If you want a bit more mathematical explicitness in your definition, a principal component is an eigenvector of a covariance or correlation matrix (Bookstein et al, 1985).) The percentage of variation explained by each PC axis should be included in the PC plot. Plots can be of the first and second axes (thus explaining the greatest variation in the data set) or of any combination of the axes, such as the 3rd and 5th axes, giving a 2-dimensional window on a surface in multivariate space.

Alternative form for Principal components analysis : PCA.