http://i277.photobucket.com/albums/k...8/DSC00004.jpg

Please help me with this question.

Does anyone know how it ends up with 2 lambda*x transpose*A equal to zero?? I don't understand how the number 2 came up!! Thanks for any help.

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- Jan 24th 2010, 04:37 AMkinkojunLagrange's Method
http://i277.photobucket.com/albums/k...8/DSC00004.jpg

Please help me with this question.

Does anyone know how it ends up with 2 lambda*x transpose*A equal to zero?? I don't understand how the number 2 came up!! Thanks for any help. - Jan 24th 2010, 05:51 AMHallsofIvy
Well, it

**doesn't**"end up with 2 lambda*x transpose*a equal to zero"! It ends up with m**plus**that equal to 0.

As to where the "2" came from, it is essentially from differentiating a square. Or you might prefer to think of it as using the product rule.

Your Lagrangian is $\displaystyle L= mx+ \lambda(x^TAx- 1)$. Differentiating $\displaystyle x^T A x- 1$, with respect to x, gives $\displaystyle Ax+ x^TA$ and, since $\displaystyle Ax= x^TA$, that is the same as $\displaystyle 2x^TA$. - Jan 24th 2010, 06:29 AMkinkojun
I was actually doubting whether differentiating $\displaystyle x^T$ is actually same as differentiating $\displaystyle x$. It seems that they are the same in term of differentiation even though it is transposed. Thank you.

As a further question in this particular case, I have uploaded an example from my text book which i could not understand the last part of it.

http://i277.photobucket.com/albums/k...8/DSC00007.jpg

http://i277.photobucket.com/albums/k...8/DSC00006.jpg

http://i277.photobucket.com/albums/k...DSC00009-1.jpg

1st pic is connected with the 2nd picture and follow up by the 3rd picture. In particular, I could not understand the whole part of the example in the 3rd pic after finish proving the equation in the 2nd pic. Could you please explain how it works in the 3rd pic. Thank you very much. (Wink)