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| -rw-r--r-- | FuVar.tex | 8 | ||||
| -rw-r--r-- | build/FuVar.pdf | bin | 161858 -> 161958 bytes |
2 files changed, 4 insertions, 4 deletions
@@ -155,7 +155,7 @@ typesetting may trick you into thinking it is rigorous, but really, it is not. \(\vec{r}\) (with \(|\vec{r}| = 1\)) given by \[ \frac{\partial f}{\partial\vec{r}} - = \nabla\vec{r} f = \vec{r} \dotp \grad f + = \nabla_\vec{r} f = \vec{r} \dotp \grad f \] \end{definition} @@ -270,13 +270,13 @@ typesetting may trick you into thinking it is rigorous, but really, it is not. \end{remark} \begin{method}[Quickly find the eigenvalues of a \(2\times 2\) matrix] - Let + This is a nice trick. For a square matrix \(\mx{H}\), let \[ m = \frac{1}{2}\tr \mx{H} = \frac{a + d}{2} , - \qquad + \quad p = \det\mx{H} = ad - bc , \] - then \(\lambda = m \pm \sqrt{m^2 - p}\). + then \(\lambda_{1,2} = m \pm \sqrt{m^2 - p}\). \end{method} \begin{method}[Search for a constrained extremum in 2 dimensions] diff --git a/build/FuVar.pdf b/build/FuVar.pdf Binary files differindex 000648d..7d3c587 100644 --- a/build/FuVar.pdf +++ b/build/FuVar.pdf |