Mathematik-Online problems: Problem 46: Proof of the Associativity of Maps

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	Mathematik-Online problems:
	Problem 46: Proof of the Associativity of Maps

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)

Show the associativity of the composition of maps, i.e.

$\displaystyle (\alpha\circ\beta)\circ\gamma=\alpha\circ(\beta\circ\gamma)$

holds for maps $\alpha, \beta, \gamma$ , for which the composition exists.

b)

Use a) to show, that

holds for all $A\in\mathbb{R}^{k\times\ell}$ , $B\in\mathbb{R}^{\ell\times m}$ and $C\in\mathbb{R}^{m\times n}$ .

(Authors: Kimmerle/Höfert)

Solution:

automatisch erstellt am 14. 10. 2004