Every eigenvalue of a square matrix lies within at least one of a set of disks in the complex plane, each centered at a diagonal entry with radius equal to the sum of the absolute values of the other entries in that row. Named for Semyon Gershgorin, it gives a quick way to localize eigenvalues without computing them exactly.
Facts
StatementEvery eigenvalue of a complex square matrix A lies within at least one Gershgorin disc D(a_ii, R_i), the disc centered at diagonal entry a_ii with radius R_i equal to the sum of the absolute values of the other entries in row i. 1 Classification
Statement Form Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Gershgorin circle theorem (Wikipedia)
Wikimedia FoundationLead section, first sentence
In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix.
Lead section, second sentence
It was first published by the Soviet mathematician Semyon Aronovich Gershgorin in 1931.
View the Source Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.