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Definitions are generalized all the time in mathematics. If Minkowski discovered something that was similar to a norm but not quite, that may be interesting, bu
by Tainnor 2y ago
Definitions are generalized all the time in mathematics. If Minkowski discovered something that was similar to a norm but not quite, that may be interesting, but it's still not a norm.
It also has nothing to do with the complex numbers where the canonical norm is, in fact, a norm.
- rhelz 2y agoThe Minkowski Norm is, in fact, a norm: https://en.wikipedia.org/wiki/Minkowski_norm https://en.wikipedia.org/wiki/Minkowski_norm // It also has nothing to do with the complex numbers // The author of the linked article said that what he was describing was a norm because it satisfied the triangle inequality (among other things). I'm just pointing out that the (among other things) was enough for it to be a norm. I certainly wished somebody had pointed out to me that not all norms need to satisfy the triangle property. There have been spaces where I wasted months of effort trying to find a norm which satisfied the triangle inequality, when a more minkowski-like norm would have been perfectly adequate.
- Tainnor 2y agoYou're playing semantic games. If it doesn't satisfy the triangle inequality it's a quasi-nonorm. When you say "norm", people understand it to imply the triangle inequality. That doesn't mean that spaces without a proper norm are useless. Also your link links to a disambiguation page.