Let's say my eigenvalue λ=-1 and we assume eigenvector of zero are non-eigenvector.(adsbygoogle = window.adsbygoogle || []).push({});

An eigenspace is mathematically represented as E_{λ}= N(λ.I_{n}-A) which essentially states, in natural language, the eigenspace is the nullspace of a matrix.

N(λ.I_{n}-A) is a matrix.

Would it then be valid to say that the eigenspace, E_{λ}, whose eigenvalue, λ=-1, is the nullspace of the matrix, N(λ.I_{n}-A), is equivalent to the the vector , v, where

Av = 0.

If v is the nullspace of the matrix A then Av = 0, and similarly, if E_{λ}is the nullspace of a matrix, N(λ.I_{n}-A), then, it must equally be true that

[ N(λ.I_{n}-A) ] [E_{λ=-1}] = 0

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# Eigenvalue, Eigenvector and Eigenspace

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