Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 68

Optimisation of norm of matrices without the elements on diagonals

Let $A in mathbb{R}^{n times n}$ be a symmetric, non-definite matrix. My general problem is to solve $$begin{array}{ll} underset{Z in mathbb{R}^{n times d}}{text{minimize}} & displaystylesum_{ineq j} left( A_{i,...

Asked on 11/26/2021 by NikoWielopolski

0 answer

Given $frac{z_1}{2z_2}+frac{2z_2}{z_1} = i$ and $0, z_1, z_2$ form two triangles with $A, B$ the least angles of each. Find $cot A +cot B$

If $z_1$ and $z_2$ are two complex numbers satisfying$frac{z_1}{2z_2}+frac{2z_2}{z_1} = i$ and $0, z_1, z_2$ form two non-similar triangles. $A, B$ are the least...

Asked on 11/26/2021 by SEO

2 answer

Notation for "and"

Consider the real numbers $a$ and $b$. I would like to express in math notation, that $c = 2$ if $a > 0$ and $b...

Asked on 11/26/2021

1 answer

Proving that, given a surjective linear map, a set is a generator of a vector space

I know how to prove that, given $L: V rightarrow W$ to be an injective linear map and ${v_1, v_2, ..., v_n}$ to be a linearly independent set...

Asked on 11/26/2021 by JD_PM

1 answer

Production function problem (Lagrange multiplier)

I want to solve this production function using Lagrange multiplier $$begin{equation}begin{aligned}max_{} quad & U(x)=(sum_{i=1}^{n}{theta_{i}x_{i}^{rho}})^{frac{1}{rho}} \textrm{s.t.} quad & sum_{i=1}^{n}{p_{i}x_{i}=I}\end{aligned}end{equation}$$What I have been doingApply lagrangian$$L(x_i,...

Asked on 11/26/2021

1 answer

Brezis-Kato regularity argument - Some questions about Struwe's proof Part II

The following is in Appendix B of Struwe's Variational Methods Let $u$ be a solution of $-Delta u = g(x, u(x))$ in a domain $Omega subset mathbb...

Asked on 11/26/2021 by Danilo Gregorin Afonso

1 answer

Understanding the multidimensional chain rule

I have some trouble in understanding the multidimensional chain rule. For differentiable functions $f,g$, defined by $f: U to V$, $g:Vtomathbb K^n$ where $U subseteq mathbb...

Asked on 11/26/2021 by ATW

1 answer

Prove identity matrix with singular value decomposition

Let $I_d$ denote the $d times d$ identity matrix and for $X in mathbb{R}^{mtimes n}$ and $lambda>0$ I have to prove the following: $$(X^TX+lambda I_n)^{-1}X^T=X^T(XX^T+lambda...

Asked on 11/26/2021 by Hojas

1 answer

Number of possible n-towers

This question is inspired by Q5 from the 2018 MAT, but it is not the same.An $n$-brick is defined as a rectangle with height $1$ and width ...

Asked on 11/26/2021 by Aatish Five

1 answer

Convergence of $sqrt{1-sqrt{{1}-sqrt{{1}-sqrt{{1-sqrt{{1}}}...}}}}$

Recently, as is evident from many of my recent questions, I have been very interested in nested radicals. Recently I attempted to investigate the following infinite nested radical and arrived...

Asked on 11/24/2021

1 answer

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