MathAlgebraLinear algebraVectors and vector spaces

Vector norm and distance between vectors

Norm or not?

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Imagine that you have a function, which has the following properties:

$\|l\cdot\vec{b}\|=|l|\cdot\|\vec{b}\|$ for any scalar $l$ and vector $\vec{b}$
$\|\vec{a}+\vec{b}\| \leq \|\vec{a}\|+\|\vec{b}\|$ for two different vectors $\vec{a}$ and $\vec{b}$ .

Can this function be a norm?

Select one or more options from the list

Triangle inequality is missing

Yes, it satisfies all properties

Zero only for zero vector property is missing

Scalar multiplication is missing

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