SVD for PCA: Why would one standardize the data matrix? [duplicate]

As explained in amoeba's beautiful answer here one can use a singular value decomposition of the data matrix, $\mathbf{X} = \mathbf{USV}^\top$, to do a principal component analysis, if it is assumed that the data matrix $\mathbf{X}$ is centered. The principal directions will then be given as the columns of $\mathbf{V}$.

Now, I have come across some statistical analysis where the data matrix was centered and standardized for the data to have unit variance before being used in a singular value decomposition. The analysis then proceeded in using the columns of $\mathbf{V}$ as principal directions.

Can any of you think of a reason to do this standardization step before running the singular value decomposition? Is the result of such a procedure in terms of what PCA should tell you even meaningful?

• This is indeed a duplicate but +1 for a clear and well-formulated question. Sep 15, 2016 at 17:02