- #1

perplexabot

Gold Member

- 329

- 5

Hey,

I have been trying to figure out how to solve [itex]\triangledown_x ||f(x)||^2_2[/itex].

I have used the chain rule (hopefully correctly) to get the following:

[tex]\triangledown_x ||f(x)||^2_2=2\triangledown_xf(x)^T \frac{f(x)^T}{||f(x)||_2}[/tex]

Is this correct?

The reason I doubt my answer is because I know the gradient of a scalar valued function should be a vector. My answer seems to give a scalar. Can anyone please shed some light...

Note: [itex]x \in \Re^n[/itex] and I am using the convection that the gradient, [itex]\triangledown_x[/itex], of a function is a row vector. Also assume [itex]f: \Re^n\rightarrow \Re^m[/itex] .

I have been trying to figure out how to solve [itex]\triangledown_x ||f(x)||^2_2[/itex].

I have used the chain rule (hopefully correctly) to get the following:

[tex]\triangledown_x ||f(x)||^2_2=2\triangledown_xf(x)^T \frac{f(x)^T}{||f(x)||_2}[/tex]

Is this correct?

The reason I doubt my answer is because I know the gradient of a scalar valued function should be a vector. My answer seems to give a scalar. Can anyone please shed some light...

Note: [itex]x \in \Re^n[/itex] and I am using the convection that the gradient, [itex]\triangledown_x[/itex], of a function is a row vector. Also assume [itex]f: \Re^n\rightarrow \Re^m[/itex] .

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