MHB Matrix L1-Norm: Max of Column Sums Explained

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The discussion centers on a homework problem regarding the l1-norm of an m x n matrix A, specifically that it equals the maximum of the sums of the columns. The original poster attempted to demonstrate this by using the definition of the vector l1-norm but ended up showing that the l1-norm equals the sum of the row sums instead. They are seeking assistance in identifying where their reasoning went wrong. Participants are encouraged to provide guidance and clarify the correct approach. The conversation emphasizes the importance of understanding the definitions and properties of matrix norms.
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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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