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A biplot simultaneously plots information on the observations and the variables in a multidimensional dataset.
A 2-dimensional biplot represents the information contained in two of the principal components. It is an approximation of the original multidimensional space.
The classical biplot (Gabriel 1971) plots points representing the observations and vectors representing the variables.
A more recent innovation, the PCA biplot (Gower & Hand 1996), represents the variables with calibrated axes and observations as points allowing you to project the observations onto the axes to make an approximation of the original values of the variables.