eigen-
combining form
characteristic; proper
⇒
eigenvalue
Origin
from German, literally: owneigen-
combining form
- Mathematics & Physics proper; characteristic【数, 物理】表示“本征”, “特征”, “固有”：
-
eigenfunction.
词源
from the German adjective eigen 'own'.
1930 Eigenstate . [ see eigenvalue]
1940 Chambers's Techn. Dict. 283/1Eigenperiod, eigenton, frequencies at which acoustic resonance is experienced in rectangular chambers, because of continued reflections between opposite walls.
1947 Jrnl. R.Aeronaut. Soc. LI. 204A complete theory of the conditions for the existence, and the form of the self-equilibrating orthogonal and load systems (eigenloads)..which vary similarly along all generators, is given.
1951 Rev. Mod. Physics 1 (title)Approximate eigen-solutions.
1955 Electronic Engin. XXVII. 200An infinite line of similar quadripoles each with matrix A connected in cascade.. must be a vector such that the effect of operating on it with A is to leave it unaltered except for a change in magnitude... Any vector..fulfilling this condition is called an eigen-vector of the operator matrix H.
1955 W. Pauli Niels Bohr 39The transformation..can be interpreted as replacing every emission operator by an absorption operator of the same eigen-vibration without interchange of particle and anti⁓particle.
1955 H. B. G. Casimir in W. Pauli Niels Bohr 131The remarkable feature of Bose–Einstein condensation is that a sizable fraction of the particles is forced into the very lowest eigenstate, a state which should have curious and essentially non-classical properties.
1957 L. Fox Two-point BoundaryProbl. vii. 162Third, if the vector y is an approximation to any eigenvector yk, so that, in 18, αk is much greater than any other αr, then first-order changes in y give rise to second-order changes in λ, and the eigenvalue is determined more accurately than its eigenvector.
1968 C. G. Kuper Introd. Theory Superconductivity ix. 150Likewise, b{caret}ϕn is either zero or an eigenstate with energy En - ℏω.
ORIGIN: German eigen own adjective .
eigen-
Prefix
- linear algebra Forms terms pertaining to or related to eigenvectors, eigenvalues; especially for naming mathematical objects which are not affected by a given transformation except for by scalar multiplication.
Etymology
From German eigen ("own"). Many of the compounds represent partial translations from German, e.g. eigenvalue from the German Eigenwert.
See also
Derived terms
English words prefixed with eigen-