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-rw-r--r-- | ClassJune26.page | 11 |
1 files changed, 5 insertions, 6 deletions
diff --git a/ClassJune26.page b/ClassJune26.page index 18f2292..0d8d588 100644 --- a/ClassJune26.page +++ b/ClassJune26.page @@ -137,8 +137,8 @@ b\end{array}\right)$ itself, and the second column is the image of $i=\left(\beg 1\end{array}\right)$, which is $\rho$ rotated by $90^{\circ}$, which has coordinates $\left(\begin{array}{c} -b\\ -a\end{array}\right)$. So complex number $a+bi$ is identified with the matrix $ -\left(\begin{array}{cc} +a\end{array}\right)$. So complex number $a+bi$ is identified with the matrix +$\left(\begin{array}{cc} a & -b\\ b & a\end{array}\right).$ As a sanity check, note that $i$ corresponds to $\left(\begin{array}{cc} @@ -218,14 +218,13 @@ means that $\left(\begin{array}{c} \frac{\partial u}{\partial y}\\ \frac{\partial u}{\partial y}\end{array}\right)$ is $\left(\begin{array}{c} \frac{\partial u}{\partial x}\\ -\frac{\partial v}{\partial x}\end{array}\right)$ rotated by $\pi/2$. If we write \[ -\left(\begin{array}{c} +\frac{\partial v}{\partial x}\end{array}\right)$ rotated by $\pi/2$. If we write +$\[\left(\begin{array}{c} a\\ b\end{array}\right)=\left(\begin{array}{c} \frac{\partial u}{\partial x}\\ \frac{\partial v}{\partial x}\end{array}\right)$ -, then $ -\left(\begin{array}{c} +, then $\left(\begin{array}{c} \frac{\partial u}{\partial y}\\ \frac{\partial u}{\partial y}\end{array}\right)=\left(\begin{array}{c} -b\\ |