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Math Help - [SOLVED] Induced matrix norms

  1. #1
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    Gold Coast, Queensland, Australia
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    [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.

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  2. #2
    Member
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    Mar 2009
    From
    Gold Coast, Queensland, Australia
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    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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