Linear Algebra : The Hessian

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

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Example Question #1 : The Hessian

Set up a Hessian Matrix from the following equation,

 

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Explanation:

Recall what a hessian matrix is:

 

         

 

Now let's calculate each second order derivative separately, and then put it into the matrix.

 

Now we put each entry into its place in the Hessian Matrix, and it should look like

 

 

Example Question #2 : The Hessian

Find the Hessian of the following function.

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Explanation:

Recall the Hessian

   

 

So lets find the partial derivatives, and then put them into matrix form.

      

 

Now lets put them into the matrix

 

 

 

 

Example Question #3 : The Hessian

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Example Question #5 : The Hessian

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Example Question #6 : The Hessian

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Example Question #7 : The Hessian

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Example Question #8 : The Hessian

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Example Question #9 : The Hessian

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Example Question #10 : The Hessian

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