[SOLVED] Induced matrix norms

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April 21st 2009, 06:23 AM
Bucephalus

[SOLVED] Induced matrix norms

Consider the matrix

$<br /> A = \left[\begin{matrix}1 & -2\\1 & 3\end{matrix}\right]<br />$

Consider the matrix norm $||\cdot||_{ind}$ induced by the $1-norm$ on the domain and the $\infty-norm$ on the range. Applied to A, we have that:
a) $||A||_{ind}=5$
b) $||A||_{ind}=\sqrt{15}$
c) $||A||_{ind}=4$
d) $||A||_{ind}=3$

thanks again.
April 22nd 2009, 10:06 PM
Bucephalus

I think I found the solution

I found a paper by Drakakis, K.
International Journal of Algebra, Vol. 3, 2009, no. 5, 231 - 240

$||A||_{(1,\infty)}=^{max}_{(i,j)|\in\{1,.....,m\}\ times\{1,.....,n\}}|a_{ij}|$

I used this formula and came up with the answer 3.
If there are no objections I will mark this one solved.

Bucephalus

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