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comment Intersection of Eigenvectors and Multivariable Calculus
In multivariable calculus, the derivative is a linear transformation. (This is one reason we care about linear transformations in the first place.) And whenever we are interested in linear transformations, we are likely to be interested in eigenvalues and eigenvectors. So I wouldn't say the two subjects seem very unrelated.
Apr
21
comment Augmented Lagrangian Method for Inequality Constraints
Tangential question, but what do you need to know this for? What problem do you want to solve?
Apr
21
comment Show that f(x) is convex
By the way, $f$ is called the "infimal convolution" of $g$ and $h$. The infimal convolution is a standard topic in convex analysis books (in case you want to learn more about it).
Apr
20
comment What should I learn to increase my skill to find proof?
So when $N = 3$, and $a_i = 1$ for all $i$, would your formula say that $(x_1 + x_2 + x_3)^2 = (x_1 + x_2)^2 + (x_1 + x_3)^2 + (x_2 + x_3)^2$? But that formula isn't true.
Apr
20
comment Is there an easier way to find the inverse of a 3x3 matrix?
Why do you need to find the inverse of a $3 \times 3$ matrix anyway?
Apr
20
comment Explain why $e^{i\pi} = -1$ to an $8^{th}$ grader?
One thing that you might be interested in learning is that multiplying by $ e^{i \theta}$ simply rotates counter clockwise by $\theta $ radians. And rotating by $\pi $ radians points you in the opposite direction, the same as if you were multiplied by $-1$.
Apr
20
comment intuition behind subspace of $R^n$
Is $ c $ a vector? What do you mean by $ P_c (x) $ ?
Apr
20
comment intuition behind subspace of $R^n$
Every subspace contains the origin, but not every linear manifold contains the origin. The term "linear manifold" sounds complicated, but it's just a translation of a subspace.
Apr
19
comment What should I learn to increase my skill to find proof?
But I am worried that the tensor product idea is actually too fancy / complicated. When $N = 1$, isn't the right hand side equal to $(2 a_1 x_1)^2$? It's possible that I'm misunderstanding what you mean by $S$. When $N = 1$, I think $S$ has a single element, which is the ordered pair $(1,1)$.
Apr
19
comment What should I learn to increase my skill to find proof?
One rule of thumb is to try simple examples. What happens in the case where $ N =1$?
Apr
18
comment MatLab Single Value Decomposition
What happens if you convert colorimage to double immediately after reading it in? Also, should rgb2bw be rgb2gray?
Apr
18
comment MatLab Single Value Decomposition
It's actually called the "singular value decomposition".
Apr
18
comment create zero-order hold in matlab
What is a zero order hold? What are your thoughts about what might be wrong?
Apr
18
comment Tangent plane of a convex set.
What do you mean by normal vector though, for example if $\Omega$ is a square? There might not be a unique normal vector.
Apr
17
comment Searching for a function where the inverse exists in a neighborhood of a point, but the Jacobian is zero.
@user3016098 In this case the Jacobian is a $2 \times 2$ matrix, not a scalar.
Apr
17
comment Searching for a function where the inverse exists in a neighborhood of a point, but the Jacobian is zero.
Well, if $f: \mathbb R \to \mathbb R$, then the "Jacobian" of $f$ at $x$ is just the derivative $f'(x)$. If $f(x) = 2^x$, then $f'(x) = 2^x \log(2) \neq 0$. So, that example actually doesn't work.
Apr
17
comment Tangent plane of a convex set.
What do you mean by tangent plane?
Apr
17
comment Searching for a function where the inverse exists in a neighborhood of a point, but the Jacobian is zero.
As a warmup problem, what if $ f:\mathbb R \to \mathbb R $ ?
Apr
17
comment How do I apply this PDE as an image filter?
No you misunderstood my comment -- I think your question is definitely on topic here. This is a good place to ask your question. I made that comment because someone else voted to close.
Apr
16
comment How do I apply this PDE as an image filter?
This is definitely an applied math question and so I think it's on-topic for this site.