- #1

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[tex]

\mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n [/tex]

Then df is what? the jacobian matrix of partial derivatives?

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- #1

- 33

- 0

[tex]

\mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n [/tex]

Then df is what? the jacobian matrix of partial derivatives?

- #2

quasar987

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More generally, suppose the map

[tex]f:U\rightarrow\mathbb{R}^n[/tex]

In differential geometry, we define on each point

[tex]

TU:=\bigcup_{x\in U}T_xU

[/tex]

Then

- #3

HallsofIvy

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Strictly speaking, df is the linear transformation that best approximates f (in the same way that y= mx+ b best approximates f(x) at x= a when m= f'(a)). Given the standard bases for R

[tex]

\mbox{f} : \mathbb{R}^m \mbox{ to } \mathbb{R}^n [/tex]

Then df is what? the jacobian matrix of partial derivatives?

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