18 lines
498 B
TeX
18 lines
498 B
TeX
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\documentclass[../../script.tex]{subfiles}
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% !TEX root = ../../script.tex
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\begin{document}
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\section{Eigenvalue problems}
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\begin{defi}
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Let $A \in \field^{n \times n}$. Then $\lambda \in \field$ is called an eigenvalue of $A$, if
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\[
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\exists v \in \field^n, ~v \ne 0: ~~Av = \lambda v
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\]
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Such a vector $v$ is called eigenvector. We call
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\[
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\set[Av = \lambda v]{v \in \field^n} =: E_{\lambda}
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\]
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eigenspace belonging to $\lambda$
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\end{defi}
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\end{document}
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