Gradients of the Determinant - Linear Algebra

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Which of the following expressions is one for the gradient of the determinant of an $n \times n$ matrix ?

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

$|A| = \sum_${i=1}^n$$(-1)^${i+j}$A_{ij}$$M_{ij}$$

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 .

Which of the following expressions is one for the gradient of the determinant of an $n \times n$ matrix ?

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

$|A| = \sum_${i=1}^n$$(-1)^${i+j}$A_{ij}$$M_{ij}$$

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 .

Which of the following expressions is one for the gradient of the determinant of an $n \times n$ matrix ?

Tap to see back →

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

$|A| = \sum_${i=1}^n$$(-1)^${i+j}$A_{ij}$$M_{ij}$$

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 .

Which of the following expressions is one for the gradient of the determinant of an $n \times n$ matrix ?

Tap to see back →

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

$|A| = \sum_${i=1}^n$$(-1)^${i+j}$A_{ij}$$M_{ij}$$

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 .