378 reputation
211
bio website
location
age
visits member for 1 year, 10 months
seen yesterday

Feb
25
awarded  Nice Question
Feb
2
awarded  Notable Question
Oct
31
revised Graduate school self-doubt (currently an undergraduate)
removed details
Oct
31
awarded  Citizen Patrol
Jun
14
awarded  Yearling
Mar
27
awarded  Popular Question
Feb
28
awarded  Nice Question
Jul
28
accepted Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?
Jul
25
awarded  Announcer
Jul
25
comment Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?
@JonasMeyer Perhaps. I've always thought that we prefer rise/run because European languages go from left-to-right then top-to-bottom, which in turn made the horizontal [respectively, vertical] axis represent the independent [respectively, dependent] variable, no? In which case, it is still, in an admittedly forceful way of pushing it, arbitrary.
Jul
25
comment Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?
@Mike Indeed! My next question is then: coincidence or design?
Jul
25
asked Why are $\sin$ and $\cos$ (and perhaps $\tan$) “more important” than their reciprocals?
Jul
19
accepted What makes elementary row operations “special”?
Jul
19
comment What makes elementary row operations “special”?
;) I discovered this a while ago, too, only to have my high school math teacher tell me I was wasting time "using less tools when I had more."
Jul
19
comment What makes elementary row operations “special”?
silly me for thinking it's finitely generated
Jul
19
comment What makes elementary row operations “special”?
Can it be (easily) proven that three is the fewest number of generators needed to obtain the entire group of invertible square matrices? Edit: It's obviously not cyclic, because multiplication is not commutative, so can we come up with two (probably more complicated) matrices that generate the three "canonical" elementary matrices? If not, why not? (I'm unfamiliar with the etiquette here, does this question scream "ask new question"?)
Jul
19
comment What makes elementary row operations “special”?
Thank you, this is the answer I needed. So in some sense, they're the "most natural" of all arbitrary generators one can come up with?
Jul
19
comment What makes elementary row operations “special”?
Just to be clear, are you saying that all linear systems with the same solution space can be obtained from one another after a finite number of elementary row operations? Or am I misunderstanding something here?
Jul
19
comment What makes elementary row operations “special”?
Yes. "Preserving the solution space" is a nice property they possess. But are these the only three operations that have this property? For one thing, we can compose them to get other such operations. My question is, what makes them so elementary?
Jul
19
asked What makes elementary row operations “special”?