Linear Algebra : Gradients of the Determinant

Study concepts, example questions & explanations for Linear Algebra

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Example Questions

Example Question #1 : Gradients Of The Determinant

Which of the following expressions is one for the gradient of the determinant of an  matrix ?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

The expression for the determinant of  using co-factor expansion (along any row) is

In order to find the gradient of the determinant, we take the partial derivative of the determinant expression with respect to some entry  in our matrix, yielding .

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