derivative of matrix
Suppose is an open set of , and for each , is an matrix. If each element in is a differentiable function of , we say that is a differentiable, and define the derivative of componentwise. This derivative we shall write as or .
In the below we assume that all matrices are dependent on a parameter and the matrices are differentiable with respect to .
For any matrix ,
where is the matrix transpose.
If are matrices such that is defined, then
When is invertible,
If are matrices and is the Hadamard product of and , then
|Title||derivative of matrix|
|Date of creation||2013-03-22 15:00:28|
|Last modified on||2013-03-22 15:00:28|
|Last modified by||matte (1858)|