eigenvalue is the scalar needed to scale the basis element of a one dimensional invariant subspace of a Linear Map to represent the behavior of the map:

\begin{equation} Tv = \lambda v \end{equation}

Note we require \(v \neq 0\) because otherwise all scalars count.

eigenvector is a vector that forms the basis list of length 1 of that 1-D invariant subspace under \(T\).

“operators own eigenvalues, eigenvalues own eigenvectors”

Why is eigenvalue consistent per eigenvector? Because a linear map has to act on the same way to something’s basis as it does to the whole space.

• New Deal

Galactica test Ka’Chava