202407200344
Status: #idea
Tags: Linear Algebra
State: #nascient

Eigenspace

The set/space that contains all the eigenvectors for a eigenvalue $\lambda$.
It is also referred to as $\lambda$-eigenspace, but when which eigenvalue is implied is clear, the lambda is often dropped.

The eigenspace is just the null space of this matrix $A-\lambda I_n$.
Note: Since an Eigenspace is always a subspace of $R^n$, the 0 vector is always in it.

Relevant theorem

You can't quite call a dot a space right? For something to be a space you need a concept of dimension. The ker(B) being equal to {0} essentially implies that the space doesn't exist, after all if your world can be spanned by nothingness, then it's not much of a world, is it?

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