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But how do you compute the derivative of x'Ax in Mathematica (x being a vector and A being a matrix)? What you have pointed out is only scalar derivatives, if I
by SoerenL 9y ago
But how do you compute the derivative of x'Ax in Mathematica (x being a vector and A being a matrix)? What you have pointed out is only scalar derivatives, if I am not mistaken here.
- improbable22 9y agoLike this, perhaps? A = {{1,2},{3,4}} vec = {x^2, x^3} D[vec.A.vec, x] Or perhaps like this, again the table of derivatives: xvec = {x1,x2} Table[ D[xvec.A.xvec,x] ,{x,xvec}] (all untested... one typo caught...)
- claar 9y agohttp://www.wolframalpha.com/input/?i=D%5B%7Bx%5E2,+x%5E3%7D.%7B%7B1,2%7D,%7B3,4%7D%7D.%7Bx%5E2,+x%5E3%7D,+x%5D http://www.wolframalpha.com/input/?i=D%5B%7Bx%5E2,+x%5E3%7D....
- parrt 9y agoAdded Link to Wolfram Alpha...
- calebh 9y agoMathematica can definitely compute the derivatives if you fix the size of the matrix. This isn't very useful if you're trying to compute the derivative of an expression with arbitrary sized matrices.
- improbable22 9y agoYou can do general matrices too, what do you have in mind? aa[x_] = {{1, 2}, {3, 4}} x bb[x_] = {x^2, x^3} D[ a[x].b[x] , x, x] (* for any suitable tensors *) % /. {a -> aa, b -> bb}