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Eigenvectors and Eigenvalues (view source)
Revision as of 12:43, June 30, 2010
, 12:43, June 30, 2010in Physics (unsourced, but I'm too lazy today - World Cup, etc)
The [[span]] of all the eigenvectors corresponding to a fixed eigenvalue <math>\lambda</math> is called the [[eigenspace]] <math>E_\lambda</math> of <math>A</math>. The dimension of this space is called the '''geometric multiplicity''' of the eigenvalue.
The [[span]] of all the eigenvectors corresponding to a fixed eigenvalue <math>\lambda</math> is called the [[eigenspace]] <math>E_\lambda</math> of <math>A</math>. The dimension of this space is called the '''geometric multiplicity''' of the eigenvalue.
== Eigenvectors and Eigenvalues in Physics ==
In Physics, eigenvectors and eigenvalues play an important role. For example, solving [[Schrödinger's equation]] (one of the fundamental equations of [[Quantum mechanics]]) is a problem of finding Eingenvectors and Eigenvalues for a very complex linear operator. The ''quantization'' (which means that discrete values are acceptable in physics, but not discrete; for example, an electron can have spin 1/2 or -1/2, but never 1/3 or 1/10) that was previously a postulated of Quantum mechanics can be derived from the fact that the eigenvalues of the operators come in discrete sets.
[[category:Linear algebra]]
[[category:Linear algebra]]