Mathematik-Online problems: Problem 70: Scalar Product, Complex/Unitary Matrices

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	Mathematik-Online problems:
	Problem 70: Scalar Product, Complex/Unitary 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

a)

Analyse if

$\displaystyle \left<x, y\right>:=\sum_{k=1}^n x_k\,y_k, \qquad \forall x=(x_1,\,\ldots , x_n),\ y=(y_1,\,\ldots , y_n)\in\mathbb{C}^n,$

defines a scalar product in $\mathbb{C}^n$ .

b)

Find a symmetric complex matrix

that is not diagonalisable.

c)

Find an unitary matrix

with $B^{-1}\neq B^{\rm {t}}$ .

(Authors: Kimmerle/Höfert)

automatisch erstellt am 12. 8. 2008