eigenvalue

[ ahy-guhn-val-yoo ]

noun

, Mathematics.

1. characteristic root.

eigenvalue

/ ˈaɪɡənˌvæljuː /

noun

1. maths physics one of the particular values of a certain parameter for which a differential equation or matrix equation has an eigenfunction. In wave mechanics an eigenvalue is equivalent to the energy of a quantum state of a system

Word History and Origins

Origin of eigenvalue¹

1925–30; partial translation of German Eigenwert, equivalent to eigen- characteristic, particular + Wert value

Example Sentences

The Perron-Frobenius theorem states that for a square matrix with all positive entries, there is a unique largest real eigenvalue and that its corresponding eigenvector has positive x and y coordinates.

From Scientific American

For example, a bit flip on the first qubit will result in the measured eigenvalue of becoming −1.

From Nature

An engineer could then use a technique called eigenvalue analysis to investigate the stability of the bicycle as one might do with an aeroplane design.

From Nature

The amount by which a unit length segment pointing in this direction is stretched or shrunk is the eigenvalue.

From Scientific American