There's a statement in the paper Phatak (1997)
In most spectroscopic problems, the number of non-zero singular values is $n-1$ for $X\in \mathbb{R}^{n \times m}$ when $n\ll m$. Consequently, at most $n-1$ principal components can be extracted.
Can anyone explain why the number of non-zero singular values, in this case, is $n-1$ instead of $n$, and if this condition is only limited for spectroscopic problems?
Thank you.