Mathematik-Online lexicon: Hadamard Basis

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematik-Online lexicon:
	Hadamard Basis

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

overview

Vector $v=(1,5)^{\operatorname t}$ has the following representation with respect to the Hadamard basis $u_1=(1,1)^{\operatorname t}, u_2=(1,-1)^{\operatorname t}$ :

$\displaystyle v= 3u_1-2u_2\,.$

Thus, for its components we have

	$\displaystyle \vert c_1\vert^2 \Vert u_1\Vert^2 +\vert c_2\vert^2 \Vert u_2\Vert^2$
	$\displaystyle \qquad = \vert 3\vert^2\Vert(1,1)^{\operatorname t}\Vert^2+\vert-2\vert^2\Vert(1,-1)^{\operatorname t}\Vert^2$
	$\displaystyle \qquad = 18+8 = 26$
	$\displaystyle \qquad = 1^2 + 5^2 = \Vert v\Vert^2\,.$

(Authors: App/Burkhardt/Höllig)

[Links]

automatisch erstellt am 8. 7. 2004