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authorPrefetch2021-02-21 20:20:46 +0100
committerPrefetch2021-02-21 20:20:46 +0100
commitd33ac5f01a6599406d516edfd45b9938795cea6d (patch)
tree8bcfed4e75229ca865f51fecef9d9adbfec22cff /latex/know/concept/legendre-transform
parent61056d57fa2c4ece7377d7736c07e8b0f12bb2af (diff)
Add "Partial fraction decomposition" and "Hilbert space"
Diffstat (limited to 'latex/know/concept/legendre-transform')
-rw-r--r--latex/know/concept/legendre-transform/source.md6
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diff --git a/latex/know/concept/legendre-transform/source.md b/latex/know/concept/legendre-transform/source.md
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--- a/latex/know/concept/legendre-transform/source.md
+++ b/latex/know/concept/legendre-transform/source.md
@@ -5,9 +5,9 @@
The **Legendre transform** of a function $f(x)$ is a new function $L(f')$,
which depends only on the derivative $f'(x)$ of $f(x)$, and from which
-the original function $f(x)$ can be reconstructed. The point is, just
-like other transforms (e.g. Fourier), that $L(f')$ contains the same
-information as $f(x)$, just in a different form.
+the original function $f(x)$ can be reconstructed. The point is,
+analogously to other transforms (e.g. [Fourier](/know/concept/fourier-transform/)),
+that $L(f')$ contains the same information as $f(x)$, just in a different form.
Let us choose an arbitrary point $x_0 \in [a, b]$ in the domain of
$f(x)$. Consider a line $y(x)$ tangent to $f(x)$ at $x = x_0$, which has