bibkey: rasmussenwilliams2006gaussian authors: Carl Edward Rasmussen; Christopher K. I. Williams year: 2006 title: Gaussian Processes for Machine Learning doi: null url: https://gaussianprocess.org/gpml/chapters/RWA.pdf claim: Appendix A gives the finite Gaussian density, conditioning, matrix determinant update, inverse derivative and log-determinant derivative under the stated positive-definite hypotheses. strata_touched: [] license: citation-only triage: anchor

Finite Gaussian and log-determinant identities

The book was published by MIT Press in 2006 (ISBN 026218253X).

Appendix A.2–A.3.1, printed pages 200–202, equations (A.4)–(A.15), states these identities for finite real Gaussian vectors with symmetric positive-definite covariance or precision matrices. The determinant update and inverse derivative require the displayed inverses; the log-determinant derivative is used on the positive-definite cone.

The source15 continuation uses these formulas only as classical intermediates for its declared finite graph family. It supplies the common reference measure, units and fluctuation scale separately; no infinite-dimensional Gaussian field or physical thermal interpretation is imported from this note.