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1d
reviewed Approve Let A be an m × n matrix, and b an m × 1 vector, both with integer entries.
1d
reviewed Approve How to find the maximum and minimum of the function $f(x) = \frac{3x}{x^2 -2x + 4}$
1d
reviewed Approve Derivative $(1-x)^{-2}$
1d
revised Vector Calculus; Divergence and Stokes Question
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2d
comment Let $\alpha(s)$ be a unit speed curve in $R^2$. Show $\kappa=|\frac{d\theta}{ds}|$
Your equation (1.) is nice. My approach was not so simple.
2d
answered Let $\alpha(s)$ be a unit speed curve in $R^2$. Show $\kappa=|\frac{d\theta}{ds}|$
2d
answered Vector Calculus; Divergence and Stokes Question
Apr
14
comment Consider the following system of differential equations
If $r^2+16=0$ then $r= \pm 4i$ hence you get $\sin(4t), \cos (4t)$ as fundamental solutions for $x$. ( I have not checked your steps)
Apr
13
answered Prove that $G$ is a vector space over $\mathbb Z_2$
Apr
6
comment How to design a differential equation to match a given general solution?
Actually, I think Travis' answer is essentially the same as the one I offer here.
Apr
6
revised How to design a differential equation to match a given general solution?
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Apr
5
answered Ambiguity in definition of $C^r$ maps between manifolds
Mar
28
awarded  Nice Answer
Mar
24
comment Why is the border rank and rank different for order 3 tensors and above?
One important distinction: higher order tensors cannot be decomposed as the direct sum of symmetric and antisymmetric tensors. There are other irreducible forms. I'm not sure if this is the reason for your question, hence this is a comment. More than this, I'd like to see a lot more on the MSE about rank of a tensor in general. I have much to learn :)
Mar
23
answered How to design a differential equation to match a given general solution?
Mar
23
comment What is an Isomorphism: Linear algebra
@TravisJ Surely with respect to some structure. Perhaps $\mathbb{Z}$-grading? But, my post above is merely targeted at the boring world of characteristic zero :)
Mar
23
answered What is an Isomorphism: Linear algebra
Mar
23
comment Coefficient Matrix and Properties of $\mathcal{L}_{B}: V\rightarrow \mathbb{R}^{3}$
Well, forget about the notation, what is more important is to understand the diagrams I work through in those videos I posted. I'm not keen on reproducing them in $\LaTeX$ here (but it can be done) so, that is why I pointed to those... the matrix of the linear transformation, the coordinate change matrix, all this stuff, if you understand the diagrams then you are a slave to no one's notation. You can make your own.
Mar
23
comment Coefficient Matrix and Properties of $\mathcal{L}_{B}: V\rightarrow \mathbb{R}^{3}$
Well, have you shown in lecture or are you allowed to use a theorem from your text which states the composition of isomorphisms is an isomorphism? Your calculation shows $F$ is invertible (and hence an isomorphism of $\mathbb{R}^3$ to itself) and the coordinate mapping is certainly an isomorphism so... I'm not sure what the rules are for where you are in the course.
Mar
22
comment Formula for 2 vectors
usually we call the "size" the magnitude or length of the vector. My advice, find the Cartesian form of both given vectors then let vector addition do the thinking for you. Of course, this depends on your reason for doing this problem...