Suppose I have a linear operator of dimension n, and suppose that this operator has a non-trivial null space. That is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]A \cdot x = 0[/tex]

Suppose the dimension of the null space is k < n, that is, I can find 0 < k linearly independent vectors, each of which yields the 0 vector when the linear operator A is applied to it.

Is it fair to say that this operator then has k eigenvalues, of value 0? and that the k eigenvectors corresponding to this eigenvalue=0 are linearly independent vectors of the null space?

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# Null Space and Eigenvalues/Eigenvectors

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