Definition
Plain language
A special direction that a transformation stretches or shrinks without turning it.
As stated in the literature
A nonzero vector v for which an operator's action is scalar multiplication, Av = λv; the nonzero requirement is essential, and omitting it produces a degenerate predicate that fails to capture the intended statement.
Also called: eigenvectors
Why it matters: These special unchanging directions reveal the core behavior of a transformation, but dropping the requirement that they be nonzero breaks the whole idea.
For example, when you stretch a rubber sheet, the directions that only get longer or shorter without tilting are its eigenvectors.
Heard on the show
“And one definition in there — an eigenvector predicate — is degenerate.”Episode 101 — Treating Math Formalization Like a Codebase, and Where the Agents Cheat