MHB Matrix L1-Norm: Max of Column Sums Explained

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The discussion centers on the proof that the L1-norm of an m x n matrix A is equivalent to the maximum of the sums of its columns. The user attempted to demonstrate this by applying the definition of the vector L1-norm with a vector x, where the L1-norm of x equals 1. However, the user concluded that the L1-norm of A equals the sum of its row sums, indicating a misunderstanding in the application of the L1-norm definition. Clarification on the correct approach is sought from the community.

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gucci1
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Hi, for a homework problem I was asked to show that for an m x n matrix A, the l1-norm of the matrix is the max of the sums of the columns. What I tried to do was plug into the definition of the vector l1-norm with Ax for some x st the l1-norm of x is 1. This shows, after a bit of simplifying, the l1-norm of A is equal to the sum of the row sums of A. This is not at all what I was supposed to show, so does anyone know where I made a mistake? Thanks for any help!
 
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gucci said:
so does anyone know where I made a mistake? Thanks for any help!

Better if you show your work. At any case, have a look here.
 

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