Feynman

177 reputation

bio	website	pathintegral.org/blog
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visits	member for	4 months
	seen	Jan 27 at 19:14
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	177 reputation	bio	website	pathintegral.org/blog	visits	member for	4 months
7 badges		location			seen	Jan 27 at 19:14

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Jan 27	awarded	Tumbleweed
Jan 20	revised	Cauchy-Schwarz for metrics with arbitrary signatures "negative norm" changed to "negative inner product"
Jan 20	revised	Cauchy-Schwarz for metrics with arbitrary signatures added some more tags
Jan 20	asked	Cauchy-Schwarz for metrics with arbitrary signatures
Jan 19	awarded	Quorum
Jan 18	accepted	The most general notion of a directional derivative
Jan 18	comment	The most general notion of a directional derivative I actually tried to (informally) generalize a directional derivative by using the notion of a direction here: pathintegral.org/blog/?p=582 I did not mention it because I did not want to look like I was just advertising myself or something. I was hoping that with some formal definitions, I would be able to prove it was equivalent to some generalized notion of a derivative known to be equivalent to the standard one in $\mathbb R^n$. Thank you for the thorough answer. I learned something about generalizations too--namely that the $C'$ in my question need not be unique! +1
Jan 18	revised	The most general notion of a directional derivative minor change--better phrasing
Jan 18	asked	The most general notion of a directional derivative
Jan 17	comment	Is there/need there be a mathematical definition of a “direction”? I thought I would mention that on a Minkowski metric, I could say that the product of the "time" direction with itself is -1, so one does not have to equate the "direction product" with the cosine of an angle. I presume in its broadest sense, it is just a mapping from pairs of directions to the interval [-1,1].
Jan 17	awarded	Supporter
Jan 17	comment	Is there/need there be a mathematical definition of a “direction”? I had to read the Wikipedia article on equivalence relations (I have a relatively narrow math background), but once I understood it, I realize your definition fits my notion of a direction quite well. +1
Jan 17	accepted	Is there/need there be a mathematical definition of a “direction”?
Jan 17	revised	Is there/need there be a mathematical definition of a “direction”? added inner product space tag.
Jan 17	comment	Is there/need there be a mathematical definition of a “direction”? I could say that the reason that a unit vector is still a vector and not a direction is because a vector divided by a magnitude is still a vector. The reals are closed under division, so any time you divide a vector by a magnitude you get a new vector with a different magnitude, not a direction.
Jan 17	comment	Is there/need there be a mathematical definition of a “direction”? Yes I know. Those however are still technically vectors and can be added and subtracted as such. I was wondering whether there was any point to defining a mathematical object analogous to a unit vector without a well defined notion of addition and subtraction.
Jan 17	asked	Is there/need there be a mathematical definition of a “direction”?
Jan 15	awarded	Scholar
Jan 15	accepted	Can exterior calculus be used to solve differential equations?
Jan 14	asked	Hodge decomposition on a manifold with a nontrivial connection