Diagonalization

A general method that constructs a new object by systematically changing the diagonal components of a purported enumeration so the constructed object differs from every object in the list; used to prove nonenumerability, separations of hierarchies, or undecidability.

The process of finding a basis in which a linear operator or matrix is represented by a diagonal matrix, equivalently finding a full set of eigenvectors so that the operator acts as scalar multiplication on each basis vector.

The process and property by which a linear operator or matrix is represented, relative to some basis, by a diagonal matrix; equivalently, the ambient vector space admits a basis made of eigenvectors for the operator.