Relation between row-space and column-space vectors

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Let $A$ be any $n$ by $m$ matrix.

  • $V$ is an orthonormal vector in column-space of $A$.
  • $U$ is an orthonormal vector in row-space of $A$.

Now, why is the following relation True? $$AV=U\Sigma$$ , where $\Sigma$ is a diagonal matrix.