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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 $\epsilon$? 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' 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