Let’s outline
mat = {{313.95758323354806, 443.4761851932803,
274.8711923640176}, {443.4761851932803,
671.32551818649, 417.77978277045105},
{274.8711923640176, 417.7797827704511,
260.0520353920102}};
This matrix is Symmetric Constructive Particular based on Mathematica.
(Edit to mirror feedback) Even SymmetricMatrixQ[mat, Tolerance -> 0], returns True.
Nonetheless, once I do RandomVariate[InverseWishartMatrixDistribution[10, mat]] , I merely get $Failed. No different error warning, nor every other info… simply $Failed. Why is that?
The reply based on feedback: Truly, the matrix isn’t Symmetric, neither is it Constructive Particular, even after making it Symmetric.
Therefore the query, what is the usefulness of features like SymmetricMatrixQ and PositiveDefiniteQ which fail for a matrix which is admittedly not on the fringe of machine precision?
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