When I taught myself linear algebra using some textbooks I found that Hermitian Matrix has been mentioned quite a few times; and I see Hermitian Matrix has applications in statistics (time series analysis, etc), which is the field I have some interests in.
I've done some google search but I couldn't really find any close/direct connection between Hermitian Matrix and Complex Analysis (apart from Hermitian Function which is part of Complex Function Theory). I might have asked google incorrectly though.
As Hermitian Matrix is a complex square matrix, do I have to study Complex Analysis in order to fully understand it?
Not really. While you can do some interesting things with Hermitian matrices if you know complex analysis, you really don't need it. A knowledge of linear algebra and basic arithmetic on complex numbers should be enough to get into some good results.