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1h
comment Calculating a unit normal to the level surface at the point
The equation in the question has a negative sign on $z^2$.
1h
comment Is isotropy preserved under uniaxial compression?
Depends on the distribution. If the points were drawn from a Poisson process (i.e. each point independently of the others) then yes. In general no. For example, if the points were drawn from a blue-noise process (each point at least a certain distance away from all others) then this property will no longer hold afterwards.
18h
comment Distribution of $aXa^T$ for normal distributed vector $a$
"If $X$ is symmetric matrix, then the above is a Wishart distribution." Are you sure about that? It's the distribution of the linear combination of $n$ chi-squared random variables, but that's not the same thing.
1d
revised Graphing/visualizing a complex parametric plot without using mathematica
added 15 characters in body
1d
awarded  Enlightened
1d
awarded  Nice Answer
2d
comment Is there a simpler function with this shape?
What do you mean, "out of syllabus"?
Apr
25
comment What are some pairs of mathematically-important functions that differ only at a few points?
Then let's get this out of the way: $\lceil x\rceil$ and $\lfloor x\rfloor+1$
Apr
25
comment How to prove a regular pentagon is formed by knotting a rectangular strip of paper?
Here's a purely geometrical formulation of the problem: Let the vertices of the pentagon be labeled $PQRST$ (with $P$ being the one where edges $a$ and $e$ meet). Because $QT$ and $RS$ are opposite sides of a rectangular paper strip, they are parallel and a unit distance apart. The same is true for the pairs of line segments $PQ$ and $RT$, $QS$ and $TP$, and $QR$ and $PS$. Given this information we have to prove that the pentagon $PQRST$ is regular.
Apr
25
comment Maximization of quadratic form on a sphere
From $x^TAx+b^Tx\le \lambda_{\max}c+b^Tx$ how do you conclude that the optimum is $x=\sqrt cv_{\max}$?
Apr
23
awarded  Nice Answer
Apr
21
comment Is this reflexive, symmetric, antisymmetric or transitive?
What you have written is not the standard definition of an antisymmetric relation, unless you add the restriction that $z_1\ne z_2$.
Apr
21
comment Proof of orthogonality in the gradient descend algorithm.
It depends on how you choose $\eta$. If it is a specified constant, then the orthogonality property is not true. If instead you choose $\eta$ to minimize $E(\mathbf w_{t+1})$ at each update, then orthogonality follows from the optimality condition for $E(\mathbf w_{t+1})$.
Apr
19
comment Showing that a matrix is symmetric positive definite
Please stop adding and removing a tag just to bump the question to the front page. If you want to bring more attention to your question, read What should I do if no one answers my question?
Apr
17
comment why is the geometric mean less than the logarithmic mean?
I think you mean $\frac{b-a}{\log b-\log a}$.
Apr
17
comment What is the typical $\epsilon$?
See en.wikipedia.org/wiki/Machine_epsilon
Apr
16
comment Is the empty set a vector in every vector space?
"According to set theory, every set must contain the empty set. So I deduce that the empty set is a member of every vector space." This is false. The empty set is a subset of every set. But it is not an element of every set.
Apr
15
comment Confused about 'staircases'
see en.wikipedia.org/wiki/Psychophysics#Staircase_procedures
Apr
15
comment How does this self referencing (circular reference) equation terminate (i.e. not create a paradox?)
Consider a simpler example. Suppose you have the equation $p + \frac13 N = N$. Then you can subtract $\frac13 N$ from both sides to get $p = \frac23 N$, so now you have $N = \frac32 p$.
Apr
15
revised Existence of a “basis” for the symmetric positive definite matrices
added 7 characters in body