square eigenvectors for Singular Value Decomposition?

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This is from my textbookenter image description here

What I don't understand is, $V$ and $U$ are already square, why the textbook says "if we want to make them square"?

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No. Let us assume that $A$ is $n \times p$ in "portrait" format ($n>p$).

Then $V$ is $p \times r$ and $U$ is $p \times r$ ($r$ being the rank)