Gradients of the Determinant - Linear Algebra
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Question
Which of the following expressions is one for the gradient of the determinant of an 
matrix 
?
Which of the following expressions is one for the gradient of the determinant of an
Answer
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 
.
The expression for the determinant of
In order to find the gradient of the determinant, we take the partial derivative of the determinant expression with respect to some entry
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