8,291 reputation
21037
bio website supermath.info
location Virgina USA
age 36
visits member for 2 years, 6 months
seen 1 hour ago

I'm interested in mathematics which is used to frame physical theory. I guess that means I'm at least a little interested in just about anything.

Currently I'm trying to understand Cartan's Method of moving frames as it applies to various classification questions of low-dimensional geometry.

I also have interest in superanalysis and certain problems of hypercomplex analysis.

More generally, I'm just looking for interested students who want to exceed the status-quo of undergraduate mathematics. Ideally, our interests overlap.


4h
comment Matrix representation induced by quotient space
The quotient space identifies everything in the kernel as a single point. For your $A$ the kernel is one-dimensional, it follows that we lose one dimension. Another example, if $A$ was just a single vector glued together three times then the kernel would be two-dimensional and the quotient space would be just a one-dimensional space. More to the point, the set of vectors you list is not linearly independent in the quotient.
8h
answered Matrix representation induced by quotient space
8h
revised Matrix representation induced by quotient space
improved non-native English, I think.
2d
comment Example: Solve a Second Order Nonhomogeneous ODE with Constant Coefficients by Variation of Parameters (2R-17)
maybe you want the solution verification tag? Is the question simply: is my solution correct? That is a valid question.
2d
comment Why is the trace of the Riemann curvature tensor useful?
being that the Ricci is constructed from the Riemann, it seems unlikely it has new information, I think your question is really, what information does the Ricci make clear, what is the meaning of the Ricci tensor perhaps?
2d
comment Extending Taylor's theorem from one to several variables
it is perhaps interesting to add that the derivation of the multivariate Taylor series naturally flows from the single variate Taylor result and the chain rule. So, while this case is special, in general it is not so far removed from the nastier looking cases.
Jan
23
comment Question concerning tensors
I think that last formula is a beautiful mess. Formulas are fun.
Jan
22
comment Linearly Independent Set Proof with Cross Product
In short, exploit orthogonality of the cross product to the given set of linearly independent vectors. In higher dimensions, you can use the null space of the transpose to select normal vectors, so, while the cross product stops making sense past $n=3$, there are certainly methods to obtain normals... even perpendicularly so...
Jan
22
answered Linearly Independent Set Proof with Cross Product
Jan
22
comment Lagrange Multipliers Calculus II Question
The funny thing is you found the harder solutions, but, missed these easy ones. I can sympathize.
Jan
22
comment Lagrange Multipliers Calculus II Question
I endorse this answer :)
Jan
22
comment Lagrange Multipliers Calculus II Question
The equation $4y=2y \gamma$ has solution $y=0$. You miss that when you divide by $y$ (which is not allowed for $y=0$ case)
Jan
22
answered Lagrange Multipliers Calculus II Question
Jan
22
comment Lagrange Multipliers Calculus II Question
They came from the hell of divided zeros. Beware the beast.
Jan
21
comment Choosing a Project Topic.
seems like emailing your professor is the best solution here.
Jan
20
comment What is the best measure for matrix similarity
does there exist $P$ such that $B=P^{-1}AP$ ;)
Jan
18
comment The Hodge dual and the Moyal product related or just notation?
you might look at scitation.aip.org/content/aapt/journal/ajp/70/5/10.1119/… for some nice deformation theory which is pretty accessible.
Jan
18
answered The Hodge dual and the Moyal product related or just notation?
Jan
18
comment Universe in a single equation
@AvZ well, if the universe is Euclidean $3$-space, I suppose that will do.
Jan
17
comment Universe in a single equation
@AvZ yes I suppose, but, that block has all possible shapes in it. If you want them separate just use an infinite Cartesian product, in each slot put an equation for the curve you want.