wrong reconstruction of covariance matrix after eigenvalue decomposition

[FuZhiyu]

In utils.jl, there is a mistake in the formula below when it reconstructs the covariance matrix after eigen decomposition:

Vcov.jl/src/utils.jl

Line 8 in 912844e

return Symmetric(eigvect' * Diagonal(eigval) * eigvect)

The correct order should be:

eigvect * Diagonal(eigval) * eigvect'

i.e., the first matrix is not transposed while the last is. To quickly check,

using LinearAlgebra;
A = Symmetric(rand(3,3));
eigval, eigvect = eigen(A);
norm(eigvect * Diagonal(eigval) * eigvect' - A) < 1e-12  # true
norm(eigvect' * Diagonal(eigval) * eigvect - A) < 1e-12  # false