Expm(P, H) computes the projection of a Hermitian matrix
H from the tangent space at a Hermitian
P to the manifold of Hermitian PD matrices equipped with the affine-invariant Riemannian metric
via the exponential map as in e.g., \insertCitePFA05pdSpecEst. This is the unique inverse of the Riemannian
a Hermitian positive definite matrix.
a Hermitian matrix (of equal dimension as
1 2 3 4 5 6 7 8 9
## Generate random Hermitian matrix H <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3) diag(H) <- rnorm(3) H[lower.tri(H)] <- t(Conj(H))[lower.tri(H)] ## Generate random HPD matrix p <- matrix(complex(real = rnorm(9), imaginary = rnorm(9)), nrow = 3) P <- t(Conj(p)) %*% p ## Compute exponential map Expm(P, H)
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