0
votes
0answers
31 views

A matrix equation with real coefficients

The problem is the following: Find $\lambda$ such that $ b^{T}A\left[A^{T}A-\lambda L^{T}L\right]^{-1}L^{T}L\left[A^{T}A-\lambda L^{T}L\right]^{-1}A^{T}b-\delta^{2}<0 $ where ...
0
votes
1answer
41 views

Unit vector that maximizes or minimizes

I know by the Taylor expansion $f(x,y)$ that in order for the origin to be a minimum point, $f_{xx}$ and $f_{yy}$ have to be both positive. Which I know how to prove. I also know other methods like ...
3
votes
1answer
102 views

Eigenvalues of a symmetric matrix with Lagrange multipliers

Problem: Using Lagrange multipliers, prove that all symmetric matrices $A \in \mathbb{R}^{n \times n}$ have all real eigenvalues. Proof: Consider $f: \mathbb{R}^n \rightarrow \mathbb{R}$ defined by ...
1
vote
1answer
76 views

What is the constraint in this LaGrange Multipliers ??

$x$ and $y$ are real numbers where satisfied the equation $x^2+y^2+xy-3x-3y-9=0$ Find the max. and min. values of $x^2+y^2$ I don't know how to find the constraint
1
vote
1answer
163 views

Lagrange method - non-linear system of equations

I have to compute optimal parametres of truncated cone so that its Volume is fixed (lets say it is 1) and its surface is minimal using Lagrange method These are equations desribing my object: ...