simple math question

There has a function can be written as: y=H*[X,Y,1]'. where [X,Y,1]is known constants. I want finding the derivatives of the series of matrix H=A*[r1,r2,t]; where A is a 3 by 3 matrix,and r1,r2,t is 3 by 1 column . During the derivatives process, A ,r1,r2,t should be viewed as the variables separately. Is anyone know how to tackle it with matlab? Or just give me some tips on this.Thank you very much!

[Andrew Newell]

You want partial derivatives with respect to the matrix A? That doesn't make sense.

[LIU WEIHUA]

sorry ,I express wrong ,it's derivatives instead of partial derivatives.

Answer 1

[Alex]

If I understand correctly, you have H as a function of r1, r2, & t.

By this, you have 3 partial derivatives, dH/dr1, dH/dr2, & dH/dt.

If those 3 partial derivative are what you want, then this is done much easier on paper.

let, A be a matrix with elements aij, with i being the row and j be the column.

 (in this case, I am assuming the matrix A has only constants, folling the same steps will get you the results for variables with higher powers).

Then, H is a system of 3 equations with 3 unknowns. Looking at the first row,

a11*r1 + a12*r2 + a13*t = H1,

then dH/dr1 becomes d(a11*r1) = dH1/dr1

then dH/dr2 becomes d(a12*r2) = dH1/dr2

then dH/dt becomes d(a13*t) = dH1/dt

(the other 2 rows follow the same).

These 9 results can be combined back into a dH matrix, with each row representing one of the partial derivatives.

[Alex]

This can be explained more in depth at: http://en.wikipedia.org/wiki/Matrix_calculus