Hessian matrix of a multivariable function

Asked May 06 '23 at 09:42

Active May 06 '23 at 09:42

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I wanted to know if there is something similar to Taylor expansion for functions of form

$$f:R^n \longrightarrow R^m $$

Wikipedia gives the Jacobian for the functions of the above form, but the hessian matrix has been only defined for scalar valued functions of form $f:R^n \longrightarrow R$

So, does hessian exists for the function of form $f:R^n \longrightarrow R^m $ and can a Taylor expansion be written for them?

asked May 06 '23 at 09:42

veke

It is the same (simply, the matrix entries are in $\Bbb R^m$). You can prove it by reasoning componentwise. – Anne Bauval May 06 '23 at 09:59
See Taylor Series coordinate free form for the proper analogue of Taylor’s theorem in higher dimensions. – peek-a-boo May 06 '23 at 10:29

Hessian matrix of a multivariable function

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