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Mathematics-Online problems:

Interactive Problem 9: Singular Value Decomposition and Approximation Problem

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
Find for the matrix

$\displaystyle A=\begin{pmatrix}1 & 0 \\ 2 & 2 \\ 0 & 1 \end{pmatrix}$

the singular value decomposition and the solution $ X$ of the approximation problem
$ \vert AX-[0,1,0]^t\vert \rightarrow $ min.


Answer:

Singular values:
$ s_{1}=$ $ > \; s_{2}=$ .

Solution of the approximation problem:
$ X=\frac{1}{9} \Big[$ , $ \Big]^{\operatorname t}\; .$

   

(Authors: Höllig/Höfert)

see also:

  automatically generated: 3/12/2018