matrix determinant differentiation in tensorflow

Question

I am interested in computing the derivative of a matrix determinant using TensorFlow. I can see from experimentation that TensorFlow has not implemented a method of differen

Answer 1

I think you are confused with what is a derivative of a matrix determinant.

Matrix determinant is a function which is calculated over the elements of the matrix by some formula. So if all the elements of the matrix are numbers, you the determinant will you you just one number and the derivative will be 0. When some of the elements are variables, you will get an expression of these variables. For example:

x, x^2
1, sin(x)

The determinant will be x*sin(x) - x^2 and the derivative is 2x + sin(x) + x*cos(x). The Jacobi formula just connects the determinant with adjunct matrix.

---

In your example your matrix A consists of only numbers and therefore the determinant is just a number and the loss is just a number as well. GradientDescentOptimizer needs to have some free variables to minimize and does not have any because your loss is just a number.