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MArix derivative

  • Thread starter strokebow
  • Start date
  • #1
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Hi,

A function: f(X) = C^T*X

Where, ^T is Transpose


Then my book tells me that GRADIENT f(X) = C


Why? Why is it not GRADIENT f(X) = C^T

Where, ^T is Transpose and GRADIENT is labla (opposite to delta)

Please help!!

Thanks
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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So
[tex]C= \begin{bmatrix}a \\ b \\ c\end{bmatrix}[/tex]
[tex]C^T= \begin{bmatrix}a & b & c\end{bmatrix}[/tex]
and
[tex]C^T X= \begin{bmatrix} a & b & c\end{bmatrix}\begin{bmatrix}x \\ y \\ c\end{bmatrix}= ax+ ay+ az[/tex]

So
[tex]\nabla C^T X= \nabla (ax+ ay+ az)= \begin{bmatrix}a \\ b \\ c}\end{bmatrix}= C[/itex]
 
  • #3
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
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Why? Why is it not GRADIENT f(X) = C^T
Check the definitions; that should make it obvious.

(I should point out that when paying attention to row vectors vs. column vectors, there are two different for defining the gradient, one being the transpose of the other)
 
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