Mathematik-Online lexicon: Complex Eigenvalues of 2x2-Matrices

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	Mathematik-Online lexicon:
	Complex Eigenvalues of 2x2-Matrices

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following examples illustrate the possible cases for complex $2\times2$ -matrices.

two eigenvalues:

$\displaystyle A=\left(\begin{array}{rr}\mathrm{i}& 2\\ 2 & \mathrm{i}\end{array... ...bda_2=-2+\mathrm{i}\,,\,v_2=\left(\begin{array}{r}1\\ -1\end{array}\right)\,.$
one eigenvalue, two linearly independent eigenvectors:

$\displaystyle A=\left(\begin{array}{rr}2\mathrm{i}& 0\\ 0 & 2\mathrm{i}\end{arr... ...end{array}\right)\,, \,v_2=\left(\begin{array}{r} 0\\ 1\end{array}\right)\,.$
one eigenvalue, one eigenvector:

$\displaystyle A=\left(\begin{array}{rr}\mathrm{i}& -1\\ 0 & \mathrm{i}\end{arra... ...d \lambda=\mathrm{i}\,,\,v_1=\left(\begin{array}{r}1\\ 0\end{array}\right)\,.$

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automatisch erstellt am 25. 6. 2018