My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
October 21st, 2016, 05:15 PM   #1
Joined: Oct 2016
From: Sverige

Posts: 32
Thanks: 2

Can someone explain what Q(h,k) has to do with det(Hessian)?

Is it the same thing?

Because I'm taught that in order to find out if a point on a plane in 3D space is a saddle-point,
local max or local min, then I'll have to look at what the determinant of the Hessian matrix is.

But in all the answers it doesn't mention Hessian, it only says like:

which is positive definite quadratic form, thus the point is a local min.

From where are they getting these formulas?
What is this Q(h,k)?

Last edited by skipjack; October 21st, 2016 at 08:02 PM.
Addez123 is offline  
October 21st, 2016, 08:10 PM   #2
Global Moderator
Joined: Dec 2006

Posts: 20,835
Thanks: 2162

They probably chose that letter because it's the first letter of "quadratic". The quadratic in your example has its minimum at the origin.
skipjack is offline  
October 22nd, 2016, 07:01 PM   #3
Joined: Oct 2016
From: Sverige

Posts: 32
Thanks: 2

But the whole equation is nothing similar to the result of a hessian determinant.
What kind of stuff are they doing here?
Addez123 is offline  
October 23rd, 2016, 03:00 AM   #4
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

It would help if you told us what the function was that gave that result!
Country Boy is offline  
October 23rd, 2016, 07:41 AM   #5
Senior Member
Joined: Sep 2016
From: USA

Posts: 635
Thanks: 401

Math Focus: Dynamical systems, analytic function theory, numerics
If $A$ is a positive definite matrix, then the linear functional defined by $v \mapsto v^TAv$ is non-negative for any vector $v$. In your case, $A$ is a 2-by-2 matrix which is the Hessian for some scalar function and the above is testing that it is positive definite by evaluating the linear functional on the vector $v = (h,k)$.
SDK is offline  

  My Math Forum > College Math Forum > Calculus

dethessian, explain

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Gradient and Hessian dhhtr Differential Equations 0 May 11th, 2015 12:04 AM
Laplacian and Hessian Jhenrique Linear Algebra 1 January 6th, 2014 01:05 AM
Hessian approach matthius Calculus 0 February 20th, 2012 07:26 AM
Hessian matrix witek Linear Algebra 0 December 22nd, 2009 08:57 AM
How to get the Hessian Matrix please? ggyyree Applied Math 0 September 28th, 2008 01:53 PM

Copyright © 2019 My Math Forum. All rights reserved.