simultaneous equations

I am looking to solve two simultaneous equations for two unknown matrices of the form:

[Y1]=a1+a2[X1]+a3[X2]+a4[X1]^2+a5[X2]^2+a6[X1][X2]

[Y2]=b1+b2[X1]+b3[X2]+b4[X1]^2+b5[X2]^2+b6[X1][X2]

Where [Y1] & [Y2] are known matrices, [X1] & [X2] are unknown matrices and a1 to a6 & b1 to b6 are scalar coefficients.

Could anyone suggest how I might go about doing this in Matlab?

Cheers,

Joe

[Chaowei Chen]

My quick bet is to vectorize [Y1], [Y2], [X1], [X2].

One question I am not sure about is [Xk]^2 and [X1][X2].

Are they regular matrix multiplication or element-by-element multiplication?

But either way, vectorization still works if I understand your question correctly. For example, your [Y1] is a 2 by 2 matrix. You can vectorize

[Y1]=a1+a2[X1]+a3[X2]+a4[X1]^2+a5[X2]^2+a6[X1][X2]

into 4 equations.

Just write out and compare each element on left and right side of the equations.