Isposdef or isspd?


#1

The docs say:

help?> isposdef
search: isposdef isposdef!

  isposdef(A) -> Bool

  Test whether a matrix is positive definite.

     Example
    ≡≡≡≡≡≡≡≡≡

  julia> A = [1 2; 2 50]
  2×2 Array{Int64,2}:
   1   2
   2  50
  
  julia> isposdef(A)
  true

But the following matrix (c.f. Wikipedia) is not correctly identified as positive definite:

julia> M = [1 1;-1 1]
2×2 Array{Int64,2}:
  1  1
 -1  1

julia> isposdef(M)
false

There is some confusion in the literature about whether a positive definite matrix is also symmetric (or more generally Hermitian), but this could be clarified by introducing isspd (or some other name).


#2

The main question is, what would this be useful for? SPD matrices have a whole branch of LAPACK dedicated to them. Not sure non-symmetric positive matrices have any nice properties that could be used for algorithms?