- #1

- 123

- 0

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

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- Thread starter strokebow
- Start date

- #1

- 123

- 0

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

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,847

- 969

[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

- 14,950

- 19

Check the definitions; that should make it obvious.Why? Why is it not GRADIENT f(X) = C^T

(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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