$ F= || AG(CoB)^T -X ||^2_f $ eq:1; Here A(i, p), G(p, qr), C(k, r), B(j, q), X(i, jk) are matrices with dimension inside respective parenthesis. ^T is matrix transpose and "o" is kronecker product. The expression is frobenius norm of matrix expression. I need to find the derivative of this expression (F) w.r.t. matrix A. Taking the help of matrixcookbook, frobenius norm derivative link, second order derivative link, I tried solving derivative of F w.r.t. A, (I am new to this field of finding matrix derivatives) and expanded but found another expression that I found difficult to differentiate w.r.t. A ie $ trace( (CoB)G^TA^TAG(CoB)^T ) $ eq:2. My answer for eq:2 is $ A(G(CoB)^T+((CoB)G^T))(CoB)G^T $. Am I doing some mistakes? Please help me in finding derivatives of eq:1 and eq:2 (w.r.t. A) and understanding the procedure for this.
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Calculating the derivative wrt $A$ of $;|AY-X|F^2;$ doesn't require us to "peek inside" the $Y$-matrix. The fact that $Y$ is constructed from Kronecker products or Hadamard products (or **_whatever**) is completely irrelevant. Don't get distracted by such things. Likewise with $;{\rm Tr}(Y^TA^TAY).$ – greg Sep 11 '19 at 16:02
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Thank you, this is helpful. – Manish Bhanu Sep 13 '19 at 07:20