epädiagonaalisina

Epädiagonaalisina is a Finnish term meaning “as non-diagonal.” It is used to describe parts, terms, or structures that do not lie on the main diagonal of a square matrix or do not follow a diagonal pattern in a coordinate system. In mathematical and technical writing, the concept commonly refers to off-diagonal elements or components.

In linear algebra, a matrix is diagonal if all off-diagonal elements are zero. The entries with i ≠ j are off-diagonal, and when they are nonzero, the matrix is not diagonal. These off-diagonal parts can carry important information about interactions, couplings, or relationships between different basis states or variables. The Finnish phrase epädiagonaalisia or epädiagonaalisina is used to describe these non-diagonal elements in various grammatical forms.

In physics and related disciplines, off-diagonal terms are described as epädiagonaalisia. For example, in a Hamiltonian or a density matrix, nonzero off-diagonal terms indicate coherence or transitions between different states and often determine the dynamics of the system. Similarly, in statistical contexts, a covariance or correlation matrix is diagonal only when variables are uncorrelated; the off-diagonal (epädiagonaalisia) entries capture pairwise correlations.

Etymology: the term combines the prefix epä- meaning non-, diagonaali meaning diagonal, and a suffix such as -na to form descriptive or inflected forms in Finnish.

See also: diagonal, off-diagonal, matrix, basis, eigenbasis.