# Jacobian of Bilinear Cost Function

Could anyone help me with the Jacobian of:

Given the following Matrices: ${E}^{1}, {A}^{21}, {A}^{22}, {C}^{1}, {A}^{12}$

$F \left( {C}^{2}, {E}^{2} \right) = {\left \| {C}^{2}{E}^{1} - {A}^{21} \right \|}_{F}^{2} + {\left \| {C}^{2}{E}^{2} - {A}^{22} \right \|}_{F}^{2} + {\left \| {C}^{1}{E}^{2} - {A}^{12} \right \|}_{F}^{2}$

Pay attention to the Frobenius Norm and that all items are matrices.

Moreover, what if I want to calculate the Jacobian in resopect to every component of ${C}^{2}$ and ${E}^{2}$? For instance, what would be the derivative of ${\left \| {C}^{2}{E}^{1} - {A}^{21} \right \|}_{F}^{2}$ relative to ${C}^{2}_{1, 1}$?

Thank You.

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When you ask a question related to an earlier question, please link to the earlier question to avoid duplication of efforts. –  joriki Aug 9 '12 at 8:16
It's not clear to me what you mean by the Jacobian here. –  joriki Aug 9 '12 at 8:19