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comment Particular solutions to homogeneous diffrential equations with non-constant homogeneous term
do you intend $6^y$ or $6y$. One of these is more interesting than the other...
Feb
9
comment Basis representation of differential-form $f(x_1,x_2):=(x_1+x_2, -x_1, -x_2)^T$
what you write does not follow the form of $\alpha$ (pun partly intended). The given $\alpha$ has $N=3$.
Feb
9
comment Basis representation of differential-form $f(x_1,x_2):=(x_1+x_2, -x_1, -x_2)^T$
nicely done. I find myself doing this when faced with explicit problems. Intuitively, just plug in the formulas for the given function and calculate.
Feb
9
comment Basis representation of differential-form $f(x_1,x_2):=(x_1+x_2, -x_1, -x_2)^T$
the answer is zero since the two-dimensional domain will not support a nontrivial three-form. When you expand that definition there will be a repeated $dx_1$ and $dx_1$ or $dx_2$ and $dx_2$ hence it vanishes.
Jan
31
comment Manifolds or Complex Analysis for Algebraic Geometry?
From a big picture perspective, I'd advocate Complex Analysis since it is useful in many directions of future study, pure and applied. That said, manifold theory should not be neglected, but, it seems to me I'd do complex first given the time for both.
Jan
17
comment How can LU factorization be used in non-square matrix?
@Normal right, that makes sense... but, there still must be some power for which $P^k=I$. So, something similar to what I have currently written is possible. I wonder, is this possible for $3 \times 3$ matrix examples. Great comment, I wish I could upvote comments ( for internet pts naturally)
Jan
16
comment How can LU factorization be used in non-square matrix?
@Normal for example ? Sorry, I can't see past swap then reverse swap does nothing...
Jan
15
comment Is parallelizability equivalent to the set of vector fields being free?
Particularly, math.stackexchange.com/a/1071338/36530 shows how parallelizable and free are connected. I don't think your question is a duplicate or anything, I just thought that Q and A might be helpful as you're thinking about these things.
Jan
15
accepted how to find null space basis directly by matrix calculation
Jan
15
comment how to find null space basis directly by matrix calculation
perfect, well, nearly so, I slapped a transpose on the end just to be stupidly literal to my question. Thanks!
Jan
15
answered how to find null space basis directly by matrix calculation
Jan
15
comment List of old books that modern masters recommend
@ElChapo so long, enjoy your new digs, well, hopefully less digging this time...
Jan
15
comment Is parallelizability equivalent to the set of vector fields being free?
see math.stackexchange.com/q/1071283/36530
Jan
15
comment Are all group homorphisms of the reals also linear transformations?
Very nice explanation.
Jan
15
comment how to find null space basis directly by matrix calculation
It's closer, but, I'm looking for something where the basis appears in a matrix and no further massage of number is needed. The method you sketch is nice, but, still I have to put minus signs and think somewhat carefully to see where the entries in the rref go into the null-vectors. Don't get me wrong, your method is nice, just not what I'm looking for here.
Jan
14
asked how to find null space basis directly by matrix calculation
Jan
14
comment Book for studying Linear Algebra
I have oodles of solved stuff and resources posted at supermath.info/LinearAlgebra.html
Jan
13
comment Rigorous Textbook for Introduction to Complex Numbers/Analysis?
@Artem care to elaborate? I am curious, what is the criticism. Style, or substance? Both? A link to a critical review would suffice. Thanks!
Jan
13
revised Rigorous Textbook for Introduction to Complex Numbers/Analysis?
edited answer in view of experience past few years
Jan
12
answered Doubt in a step given in a document on Exact Differential Equations