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Linear Algebra

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From SVD to Basis for Column Space

LINALG-Q9IBTV

Suppose that $A$ is a matrix and $A= U \Sigma V^T$ is a singular value decomposition of the matrix $A$. Describe how to find a basis for the column space of $A$ using the decomposition.

A

The columns of $U$ are a basis for the column space of $A$.

B

The columns of $V^T$ are a basis for the column space of $A$.

C

The rows of $V^T$ are a basis for the column space of $A$.

D

The first $r$ columns of $U$ are a basis for the column space of $A$, where $r$ is the number of non-zero elements of $\Sigma$.

E

There is no simple way to find a basis for the column space of $A$ from a singular value decomposition.

F

None of the above.