Exercise · ZW-HESSIAN-MATRIX-010 · ★★★ Advanced
What size is the Hessian of a function \(f(x,y,z)\) of three variables?
Choose one option.
Show answer
- B. \(3\times3\)
Explanation
There is one row and one column per variable, holding the nine second derivatives \(f_{ij}\); for two variables it was \(2\times2\).
Review the concept: Hessian matrix
The Hessian matrix \(H\) of a function \(f\) of two variables is the \(2\times2\) matrix of its second-order partial derivatives at a point.
\[H=\begin{pmatrix}f_{xx}&f_{xy}\\ f_{yx}&f_{yy}\end{pmatrix}\]
More practice problems: hessian matrix
- ZW-HESSIAN-MATRIX-001 Compute the Hessian matrix of f(x,y)=x^2+3xy+y^2.
- ZW-HESSIAN-MATRIX-002 Compute the Hessian of f(x,y)=x^3y at (1,1).
- ZW-HESSIAN-MATRIX-003 Compute det H for f(x,y)=x^2+xy+y^2.
- ZW-HESSIAN-MATRIX-004 Compute the Hessian of f(x,y)=e^xy at (0,0).
- ZW-HESSIAN-MATRIX-005 Compute the Hessian of f(x,y)=xln y at (1,1).
- ZW-HESSIAN-MATRIX-006 If f has continuous second-order partial derivatives, what always holds for its Hessian H?
- ZW-HESSIAN-MATRIX-007 Compute the trace of the Hessian of f(x,y)=x^3+y^3-3xy at (1,1).
- ZW-HESSIAN-MATRIX-008 For k>0, which value makes the Hessian of f(x,y)=x^2+kxy+y^2 singular?