# Generalized SVD, full-row rank and full-column rank.

In the generalized SVD (Golub and Van Loan, 2nd Ed. pp 471-473 Section 8.7.3), and its extension the Higher Order generalized SVD(http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0028072) all of the explanations always start off with assuming a full-column rank for the matrices in question. Would the assumptions hold if the matrices were full-row rank instead of full column rank, with ofcourse shared left-basis vectors now instead of shared right-basis vectors?