Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By which I mean the unique function $\varphi' : A \rightarrow \mathrm{Sub}(X)$ defined as follows. $$\varphi'(\lambda) = \{x \in X \mid \varphi x = \lambda x\}$$
I am also interested in traditional notation for this function.