  We report on the measurement of spin density matrix elements of the
$\Lambda(1520)$ in the photoproduction reaction $\gamma p\rightarrow
\Lambda(1520)K^+$, via its subsequent decay to $K^{-}p$. The measurement was
performed as part of the GlueX experimental program in Hall D at Jefferson Lab
using a linearly polarized photon beam with $E_\gamma =$ 8.2-8.8 GeV. These are
the first such measurements in this photon energy range. Results are presented
in bins of momentum transfer squared, $-(t-t_\text{0})$. We compare the results
with a Reggeon exchange model and determine that natural exchange amplitudes
are dominant in $\Lambda(1520)$ photoproduction.
