bijesh12
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#1
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#1
I just had a lecture on matrix norms and other matrix features which i missed on friday. Now trying to attempt the worksheet, i think i've got question i) correct but completely confused by ii).

Can someone confirm whether i've got i) right, and then explain ii)

question :

for the matrix A =  \left( \begin{array}{cccc}

1 & 0 & 3 & -8 \\

4 & 2 & -5 & 2 \\

-3 & 0 & 1 & 1 \end{array} \right)\]

i) find  ||A||_1 and  ||A||_{\infty}

ii)For A =  [a_{ij}]_{m*n} . Find  x_0 such that  ||Ax_0||_{\infty} = ||A||_{\infty} and  ||x_0||_{\infty} = 1

My answers for i) are  ||A||_1 = 11 and  ||A||_{\infty} = 13
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ghostwalker
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(Original post by bijesh12)
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Not my forte, but as no-one else has replied.

From checking wiki, I agree with your answers for i).

For ii) there is a very easy answer. I'd check the definition of the infinity norm for vectors, as it's somewhat different to that for matrices.
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bijesh12
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(Original post by ghostwalker)
Not my forte, but as no-one else has replied.

From checking wiki, I agree with your answers for i).

For ii) there is a very easy answer. I'd check the definition of the infinity norm for vectors, as it's somewhat different to that for matrices.
for the vector norm  ||x_0||_{\infty} = max {|x_1|,|x_2|,...,|x_n|}
so for the previous question this equals 1, Im assuming x0 is a vector, therefore :

 ||x_0|| = 1

So the largest element in the vector x_0 is 1.

Also  ||Ax_0||_{\infty} = 13
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ghostwalker
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(Original post by bijesh12)
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It's not clear from your post, but I presume you've now solved this, unless you say otherwise.
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