Description Usage Arguments References See Also Examples

`Expm(P, H)`

computes the projection of a Hermitian matrix `H`

from the tangent space at a Hermitian
PD matrix `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
logarithmic map `Logm`

.

1 | ```
Expm(P, H)
``` |

`P` |
a Hermitian positive definite matrix. |

`H` |
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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