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I didn't know matrices had derivatives.
by bobsmooth 4y ago
I didn't know matrices had derivatives.
- hgsgm 4y agoA matrix is an array of expressions. Its derivative is the matrix of derivatives of its expressions. This is 0 for any matrix of constants, as you can see in the example.
- pid-1 4y agoTaking the derivative of a matrix is equivalent to writing a system of differential equations.
- wenc 4y agoNot really. A matrix derivative is just a derivative -- it doesn't have to be part of an equation. The derivative of x² is 2x (where x is a scalar) The derivative of vᵀv is 2v (where v is a vector) There's no differential equation.
- goalieca 4y agoIf you want to generalize it even further you can have tensor calculus. An example is each point in a field is a 3x3 matrix with a special property of positive symmetric. A diffusion tensor MRI image has one at each voxel whereas a regular mri image might have a scalar value (grayscale). The principle eigenvector might represent the direction of a muscle fibre for that Voxel.