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eigenvalue [2013/09/18 18:15] nikolaj |
eigenvalue [2013/09/18 18:15] nikolaj |
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===== Eigenvalue ===== | ===== Eigenvalue ===== | ||
==== Definition ==== | ==== Definition ==== | ||
- | | @#88DDEE: $V$...$F$-vectorspace | | + | | @#88DDEE: $V$ ... $F$-vectorspace | |
| @#88DDEE: $A\in\mathrm{End}(V)$ | | | @#88DDEE: $A\in\mathrm{End}(V)$ | | ||
- | | @#FFBB00: $\lambda\in\mathrm{EigenVal}(A)\equiv\{\lambda\ |\ \exists (v\in V).\ A\ v=\lambda\ v\}$ | | + | | @#FFBB00: $\lambda\in\mathrm{EigenVal}(A)$ | |
- | | @#55EE55: $\exists (v\in V).\ A\ v=\lambda\ v$ | | + | | @#55EE55: $\exists v.\ A\ v=\lambda\ v$ | |
==== Discussion ==== | ==== Discussion ==== |