Linear Algebra

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Number of Singular Values of a Square Matrix

LINALG-9OLA7W

Suppose that $M$ is an $n\times n$ matrix. Which of the following must be true about the number of singular values of $M$? Select ALL that apply.

A

$M$ has at most $n$ non-zero singular values.

B

If $M$ is invertible, then $M$ has exactly $n$ non-zero singular values.

C

If $M$ has exactly $n$ non-zero singular values, then $M$ is invertible.

D

$M$ has exactly $n$ non-zero singular values.

E

None of the above.