Suppose ##T## is an operator in a finite dimensional complex vector space and it has a zero eigenvalue. If ##v## is the corresponding eigenvector, then(adsbygoogle = window.adsbygoogle || []).push({});

$$

Tv=0v=0

$$

Does it mean then that ##\textrm{null }T## consists of all eigenvectors with the zero eigenvalue?

What if ##T## does not have zero eigenvalue? Does it mean that its null space is just the zero vector?

Thanks

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# B Zero eigenvalue and null space

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