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eigenvalue [2013/08/31 22:30] nikolaj created |
eigenvalue [2013/09/18 18:15] nikolaj |
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| - | ===== Vector space ===== | + | ===== Eigenvalue ===== |
| ==== Definition ==== | ==== Definition ==== | ||
| | @#88DDEE: $V$...$F$-vectorspace | | | @#88DDEE: $V$...$F$-vectorspace | | ||
| | @#88DDEE: $A\in\mathrm{End}(V)$ | | | @#88DDEE: $A\in\mathrm{End}(V)$ | | ||
| - | | @#FFBB00: $\mathrm{EigenVal}(A)\equiv\{\lambda\ |\ \exists (v\in V).\ A\ v=\lambda\ v\}$ | | + | | @#FFBB00: $\lambda\in\mathrm{EigenVal}(A)\equiv\{\lambda\ |\ \exists (v\in V).\ A\ v=\lambda\ v\}$ | |
| + | |||
| + | | @#55EE55: $\exists (v\in V).\ A\ v=\lambda\ v$ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| - | ==== Context ==== | + | ==== Parents ==== |
| === Subset of === | === Subset of === | ||
| [[Field]] | [[Field]] | ||
| === Requirements === | === Requirements === | ||
| [[Vector space endomorphism]] | [[Vector space endomorphism]] | ||
