The standard linalg function isposdef does not work for symmetric matrices (recent git master):

x = rand(5, 5)
x = x*x'
isposdef(x)
isposdef(Symmetric(x))

The last line fails with an error:

ERROR: MethodError: no method matching isposdef!(::Symmetric{Float64,Array{Float64,2}})

which I guess is caused by a missing definition. One workaround is to access underlying matrix directly but it is inconvenient:

isposdef(Symmetric(x).data)

I think this behavior is not correct and surprising for each user, I have not found any mention of such limitation in the documentation. There is an additional implementation for Diagonal matrices and this works fine:

isposdef(Diagonal(rand(1, 5)))