 10:00 AM
A new tag was created by Shootforthemoon.
0  Is there example of let's say a two variable function that can be rewritten as an explicit function of one variable but that does not satisfy the assumptions of the implicit function theorem? In fact, if the theorem only provides sufficient conditions, we should say that there exists some implic... Dini's theorem
In the mathematical field of analysis, Dini's theorem says that if a monotone sequence of continuous functions converges pointwise on a compact space and if the limit function is also continuous, then the convergence is uniform. == Formal statement == If X is a compact topological space, and { fn } is a monotonically increasing sequence (meaning fn(x) ≤ fn+1(x) for all n and x) of continuous real-valued functions on X which converges pointwise to a continuous function f, then the convergence is uniform. The same conclusion holds if { fn } is monotonically decreasing instead of increasing. The...
Two new tags and were cretaed by Ongky Denny Wijaya.
1  Given random variable $X$ with cumulative distributive function $$F_X(x)= \begin{cases} 0&x<0 \\ \dfrac{1}{4}x^2&0\leq x<1 \\ \dfrac{1}{2}&1\leq x<2 \\ \dfrac{1}{3}x&2\leq x<3 \\ 1&x\geq 3 \end{cases}.$$ Find the probability density function of $X$. To find the p.d.f, I plot the graph of F_X... A new tag was created by miosaki. 4  \begin{align} D(m_1,m_2)=\sup\limits_{G\in \mathcal L_{p}}\left[\int\limits_{\mathbb R} G dm_1-\int\limits_{\mathbb R} G dm_2\right] \end{align} where forp\in (0,1]and \begin{align} \mathcal L_p=\{f : \mathbb R\to \mathbb R: |G(x)-G(y)|\le D^{p}(x,y)\}. \end{align} Clearly (1)D(m, m)=0$f... 2  If$\pmb a$,$\pmb b$, and$\pmb c$are the three sidelengths of an arbitrary triangle, prove that the following inequality is true with the equal sign holding for equilateral triangles. Inequality in Compact Form: $$7\left(a+b+c\right)^3-9\left(a+b+c\right)\left(a^2+b^2+c^2\right)-108abc\ge0$$... It seems that triangle inequality briefly existed in 2013: math.stackexchange.com/posts/432938/revisions Queries which show also editors who added/removed the tag: data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/… A new tag was created by Na'omi. 0  I am studying the Feasible Directions Algorithm to Nonlinear Complementarity Problem FDA-NCP (see http://ns.optimize.ufrj.br/files/SandroRodriguesMazorche.pdf). At page 31, we have:$(F_i(x^k)e_i+x_i^k\nabla F_i(x^k))d^k_1=0$. where$x^k,e_i,F$are$n$-dimensional vectors and$x_i,F_i$the... A new tag was created by Rodrigo de Azevedo. He also created a tag-excerpt. There are now 13 questions with the tag. 2  If$A$is an$n \times n$Hermitian matrix, and$S$is an$n \times n$matrix, then$S A S^*$is also Hermitian. Why is this true? I have seen this claim made in several places but can't find a proof. 0  A given problem states: If$A$and$B$are Hermitian matrices, prove that$(AB+BA)$is Hermitian. Because the sum of Hermitian matrices is known to be Hermitian, the problem seems to me to boil down to proving that the products$AB$and$BA$are Hermitian. But this isn't necessarily so, unl... 1  Suppose we are given a Hermitian matrix$E \in \mathbb{C}^{n\times n}$. I want to find sufficient conditions on the entries of a real symmetric matrix$M$(depending on the entries of the given matrix$E$) such that the matrix$EM$is again Hermitian. Is there a systematic way to determine the ... 0  My TA said that every hermitian matix implies transformation is hermitian because you can find orthonormal basis for every hermitian matrix and therefore transformation is hermitian. Is that true?? What about the converse? If the transformation is hermitian, then matrix of T is hermitian? 2  If$H$be a Hermitian matrix, prove that$\det H$is real number. If$S$be a skew Hermitian matrix of order$n$, prove that (i). if$n$be even, then$\det S$is real number; (ii). if$n$be odd, then$\det S$is a purely imaginary number or zero. Attempt: 1. Let$H=P+iQ$be a Hermitian ... 0  Suppose there is a hermitian matrix. Then, Can we always find out orthonormal basis for this matrix ? And, Is there any relationship between hermitian matrix and hermitian transformation? If matrix is hermitian, does that imply transformation is hermitian? or If the transformation is her... 1  How can I generate random commuting hermitian matrices ? EDIT: Another question: given a certain hermitian matrix, how can I generate a random hermitian matrix which commutes with it? 32  Matrices such as $$\begin{bmatrix} \cos\theta & \sin\theta \\ \sin\theta & -\cos\theta \end{bmatrix} \text{ or } \begin{bmatrix} \cos\theta & i\sin\theta \\ -i\sin\theta & -\cos\theta \end{bmatrix} \text{ or } \begin{bmatrix} \pm 1 & 0 \\ 0 & \pm 1 \end{bmatrix}$$... 3  A Hermitian matrix is a complex square matrix which is equal to its conjugate transpose. Its matrix elements fulfil following condition: $$a_{ij} = \bar{a}_{ji}$$ Everytime, I compute eigenvectors of a Hermitian matrix using Python, the first coefficient of the eigenvector is a pure real number... 0  I understand that Hermitian matrices has real eigenvalues. Just to hit the point home, I have the following question. Does every Hermitian matrix has eigenvalues? Since the proof assumes that the eigenvalue exists, the proof does not imply that every Hermitian matrix must have some eigenvalues.... 4  According to Wikipedia: The product of two Hermitian matrices$A$and$B$is Hermitian if and only if$AB = BA$. So if I understood correctly, if$C=AB$, then C will be Hermitian if and only if$AB=BA$. But... I've been able to create a matrix$S$then did$R=SS^H$, and$R$turned out to... 0  this came up on a Homework I have. I had to prove that the absolute value of the determinant of a Unitary Matrix is 1. So because$\det (A^H) = \det(conjugate(A))$and$\det(A) \det(conjugate(A)) = \det(A)^2$as well as that for a Unitary Matrix$A*A^H=I$that$\det(A^H) = \pm \det(A)$This w... 3 hours later… 1:36 PM A new tag was created by Rodrigo de Azevedo. He also created a short tag-excerpt. 3  What exactly is the Perron–Frobenius theorem? In different books and papers I read different statements, and I don't know what the truth is. In Wikipedia there are also a lot of statements under this label. And if somebody can characterize the statement for me, then I need also a proof. I read t... 0  Let$A \in \mathbb R_{>0}^{n \times n}$. Consider all the eigenvalues of$A$, including complex-valued ones. Prove that the eigenvalue that has the largest absolute value is a positive real eigenvalue. I also expect the proof using just elementary linear algebra. 5 hours later… 6:18 PM A new tag was created by Nathaniel. 2  An exponential family of probability distributions is usually defined as $$p(x) = e^{\theta\cdot f(x) \,-\, \psi(\theta)},$$ where$\theta$is a vector of parameters,$f(x)$is some arbitrary vector-valued function of$x$, and$\psi= \log\sum_x e^{\theta\cdot f(x)}$, which ensures normalisation... A new tag was created by heepo. The same user also created a tag-excerpt. 1  I'm slugging my way through Ahlfors' "Some Remarks on Teichmuller Space" and am stuck on the calculation of equation (1.18). The problem here is to compute the third derivative, on the unit disk$\mathbb{D}$, of the function$\$ \Phi(\zeta) = \frac{-2}{\pi} \iint_{\mathbb{D}} \bar{\nu}(z) \frac{\z...

However, there is an already existing tag . Should there be a synonym, or should the newly created tag be simply removed?