Hessian Matrix\Max Min Analysis, Eigenvalues etc

[alec_tronn]

In my calc 3 class, we've taken an alternative(?) route to learning maxes and mins of multivariable equations. By using a Hessian Matrix, we're supposed to be able to find the eigenvalues of a function at the point, and determine whether the point is a max, min, saddle point, or indeterminant. Also, using these eigan values, a new axis system is formed. I can only vaguely understand most of what the teacher has explained (thick middle-eastern accent), and I have until Thursday to fully understand everything. Our book does not cover the matrix ways of doing things.

Does anyone have any useful links on hessian matrices? I have looked, but they all seem to go deeper into matrix things or use notation that I'm not familiar with.

Any books I should try to find (textbooks or otherwise)? Everybody got a D on the first quiz, and I'm not looking forward to that happening again on the test. Thanks for any information, links, or explanations that you can provide.

 

[quasar987]

The Hessian matrix is just the name of the matrix (read "table") in which the second order derivatives are stored. Just as the gradient vector (while written in matrix notation) is the table in which the first order derivatives are stored.

See http://en.wikipedia.org/wiki/Hessian_matrix ans particularly the "Critical points and discriminant" and "Second derivative test" paragraphs.