What does "up to proportionality" mean exactly?

Question

Using the "site:"-specific Google search, I have searched both MO and math.SE for the word, "proportionality," and have noticed the phrase "up to proportionality" in many posts.

What does "up to proportionality" mean exactly? A link to its source would be nice.

For example, a certain constant is so (i.e. constant) "up to proportionalty" because its value may change if we change the units of measure involved. — Mauro ALLEGRANZA, May 14 '17 at 14:43
"There is, up to proportionality, a unique triangle with all edges the same length." Something like that? — Arthur, May 14 '17 at 14:44

score 1 · Answer 1 · answered May 14 '17 at 14:41

Depends on context. It usually means that the answer of a problem is only well-defined up to a constant. For example when you compute an eigenvector of matrix, the vector $v$ is equivalent with the vector $5\cdot v$, so one might write a sentence like "the eigenvector is $\dots$ up to proportionality".

law-of-fives · Accepted Answer · 2017-05-14T14:57:03.170

1

"Up to" is usually used when two things only differ in superficial or removable ways relative to the focus of the discussion/proof/etc. Indefinite integrals are the same up to a constant. Lines are the same up to a choice of basis. You can find it on wikipedia's jargon page. Also it has its own page.

edited May 14 '17 at 14:57

answered May 14 '17 at 14:44

law-of-fives

1,963

2

The jargon page link is very limited in what it says about "up to". I would link the page that wikipedia has explicitly on this phrase. – Arthur May 14 '17 at 14:48

What does "up to proportionality" mean exactly?

2 Answers2