Update Cholesky factors

Description

Calculation of the cholesky factor is very expensive, which is why updating a given Cholesky factor can save substantial amount of effort. It would this be great to be able to update the Cholesky factor L of a matrix A such that you get tilde{L} for tilde{A} whenever a row and column r is removed from A.

See:
https://normalsplines.blogspot.com/2019/02/algorithms-for-updating-cholesky.html

Another common update to Cholesky factors are rank-1 updates, which would also be great to have.

Also refer to:
https://en.wikipedia.org/wiki/Cholesky_decomposition#Updating_the_decomposition

Looks like Eigen supports this out of the box:
https://eigen.tuxfamily.org/dox/classEigen_1_1LLT.html#a56b1b914d7bd101a474c325327e17049

Example

An example application is for multi-variate normal covariance matrices. When I want to subset these to a sub-space, I simply need to get rid of the r th row and column of the covariance matrix, for example. In case I already have the Cholesky factor of that covariance matrix, then it would be a lot faster to update the respective Cholesky factor rather than recomputing the full thing.

Expected Output

Current Version:

v4.5.0

The issue names no Stan Math files, tests, or entry points. Start by locating the existing Cholesky implementation and reviewing the linked Eigen LLT documentation and Cholesky update references. Done should include support for removing a row and column, plus rank-1 updates, with coverage for the requested behavior.