Reputation
Top tag
Next privilege 125 Rep.
Vote down
Badges
3
Newest
 Supporter
Impact
~782 people reached

  • 0 posts edited
  • 0 helpful flags
  • 3 votes cast
Feb
18
comment Special case of the Hodge decomposition theorem
Ah. Thanks! The general result is: for a vector $a$ and r-vector $B_r$, we have $a \cdot B_r = \frac{1}{2}(aB_r - (-1)^r B_r a)$. Hence, $a \cdot B_0 = \frac{1}{2}(aB_0 - (-1)^0B_0a) = \frac{1}{2}(aB_0 - B_0a) = 0$.
Feb
18
comment What is a covector and what is it used for?
Then don't we have: $e^3\frac{e_1 \wedge e_2}{e_1 \wedge e_2 \wedge e_3} = (e_1 \wedge e_2)(e_3 \wedge e_2 \wedge e_1) = e_3$? Or is there some subtlety?
Feb
18
awarded  Supporter
Feb
18
comment Special case of the Hodge decomposition theorem
You wrote $∇∧ϕ$ for a scalar field $ϕ$. What does the curl of a scalar field mean?
Feb
24
comment Are Clifford algebras and differential forms equivalent frameworks for differential geometry?
Can you provide references to the alternatives to Geometric Calculus that you're talking about?
Oct
28
comment What is a vector with a single non-zero component called?
Right, I'm interested in the general term, when the component is not necessarily equal to 1.
Oct
28
awarded  Student
Oct
28
asked What is a vector with a single non-zero component called?
Jan
24
asked Proof for the divisibility of natural numbers by at least one prime
Jan
24
awarded  Autobiographer