What does S^n++ mean in math?

And how to solve the question in the picture attached?

1) [2 points] Perspective of log determinant. Show that f(X, t) = ntlogt - t log det X, with domf = S?4 x R++, is convex in ( X, t). Use this to show that g(X) = n(trX) log(trX) - (trX) (log det X) n n n n Ai log Ex - Clog Ai i=1 =1 where i are the eigenvalues of X, is convex on S? 54+. Hint: Consider the function log det X and compute its perspective