I’ve never seen a norm like that. How does it preserve positive homogeneity / direct scalar proportion? If it’s an L1 norm shouldn’t it be defined with an integral?

What if your x_i are negative? Norms can’t map to C… And it also doesn’t have homogeneity… You could’ve done \vert \sum x_i \vert for the 1-norm, if you don’t like squares.

ell-one norm is |x_1|+…+|x_n|. Norms have to scale with scalar multiplication. It does give you a metric and the standard Euclidean topology, if you put absolute-value bars on all the x_i.

Um, those xi’s should be squared…

It’s not necessarily a Euclidean norm. ;)

But Norm’s a Standard member of Cheers!

I don’t think there’s any nontrivial subspace of R^n that this is a norm on, though.

it’s an ell-one norm

I’ve never seen a norm like that. How does it preserve positive homogeneity / direct scalar proportion? If it’s an L1 norm shouldn’t it be defined with an integral?

What if your x_i are negative? Norms can’t map to C… And it also doesn’t have homogeneity… You could’ve done \vert \sum x_i \vert for the 1-norm, if you don’t like squares.

ell-one norm is |x_1|+…+|x_n|. Norms have to scale with scalar multiplication. It does give you a metric and the standard Euclidean topology, if you put absolute-value bars on all the x_i.