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Say I have a diagonal line segment/vector such that the horizontal component is longer than the vertical component (or vice versa). Is there a common name / term for each of the components?

I'm looking to describe this vector using something like "the dominant axis is horizontal", or "the major component is vertical", but I'm wondering if there's some succinct mathematical term that is a better fit here.

Thank you!

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  • $\begingroup$ The $L^\infty$ norm of a vector is, by definition, the maximum absolute value of a component of a vector: $\|\mathbf{x}\|_{L^\infty} = \max\{|x_1|,\ldots,|x_n|\}$ $\endgroup$ – Artem Mavrin Dec 17 '15 at 6:01
  • $\begingroup$ @ArtemMavrin Ok, but how do you say it? $\endgroup$ – par Dec 17 '15 at 6:03
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"largest coordinate (in absolute value)" or "smallest coordinate (in absolute value)" are good options.

If you're writing something and want something shorter, you can write this first and give an abbreviation for it like LC and SC, or come up with your own term for these.

Alternatively, you could define some functions of a vector $x$, $L(x)=\arg\max_i |x_i|, S(x) =\arg\min_i |x_i|$ to denote these coordinates (not the greatest notation, but you can play around with it; you could then say the $L$-th coordinate of $x$ and $S$-th coordinate of $x$).

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