title: What is the point of the Symmetric type in Julia?
body: <p>What is the point of the <code>Symmetric</code> type in the <code>LinearAlgebra</code> package of Julia? It seems like it is equivalent to the type <code>Hermitian</code> for real matrices (although: is this true?). If that is true, then the only case for which <code>Symmetric</code> is not redundant with <code>Hermitian</code> is for complex matrices, and it would be surprising to want to have a symmetric as opposed to Hermitian complex matrix (maybe I am mistaken on that though).</p>
  
  <p>I ask this question in part because I sometimes find myself doing casework like this: if I have a real matrix, then use <code>Symmetric</code>; if complex, then <code>Hermitian</code>. It seems though that I could save work by just always using <code>Hermitian</code>. Will I be missing out on performance or otherwise if I do this?</p>
  
  <p>(Also, bonus question that may be related: why is there no <code>HermTridiagonal</code> type in addition to <code>SymTridiagonal</code>? I could use the former. Plus, it seems more useful than <code>SymTridiagonal</code> in consideration of the above.)</p>