# Zero mode

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{{short description |Eigenvector with vanishing eigenvalue}}
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In [physics](/source/physics), a '''zero mode''' is an [eigenvector](/source/eigenvector) with a vanishing [eigenvalue](/source/eigenvalue).<ref name="vau08">{{cite book |last=Vaughn |first=Michael T.
|title=Introduction to Mathematical Physics |location=Germany |publisher=Wiley |year=2008 |page=81 |isbn=9783527618859 |doi=10.1002/9783527618859 }}</ref> 

In various subfields of physics zero modes appear whenever a physical system possesses a certain symmetry. For example, [normal modes](/source/normal_modes) of multidimensional [harmonic oscillator](/source/harmonic_oscillator) (e.g. a system of beads arranged around the circle, connected with springs) corresponds to elementary vibrational modes of the system. In such a system zero modes typically occur and are related with a rigid rotation around the circle. 

The [kernel](/source/kernel_(algebra)) of an operator consists of left zero modes, and the [cokernel](/source/cokernel) consists of the right zero modes.

==References==
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Category:Linear algebra

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Adapted from the Wikipedia article [Zero mode](https://en.wikipedia.org/wiki/Zero_mode) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Zero_mode?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.