# Geometric interpretation of Cholesky Decomposition

I understand that a square matrix, say $$A$$, can be thought of as a linear transformation within the same space. I could be as simple as basis change or some other transformation.

In this way of interpretation, how to understand/make sense of Cholesky Decomposition (both classical version and LDL* Decomposition)? From an answer in quora I gather it is related to inner-product but didn't understand that too well.

I know this question can be posted on Mathematics but given the heavy use of linear algebra in Multivariate statistics, I though I might get a good answer here.

• – whuber Sep 11 '19 at 15:50
• @whuber tried reading about this. Seems too generic so maybe Cholesky is a form of this in linear algebra but it didn't really help. Thanks anyway for the reference. – Dayne Sep 12 '19 at 0:54
• The Bruhat decomposition provides a deep "geometric interpretation," as you requested. Rather than "generic" it is an insightful generalization. – whuber Sep 12 '19 at 12:16
• I actually did mean generalization by generic. Anyway, I am still looking for a rather focussed interpretation of Cholesky Decomposition. – Dayne Sep 12 '19 at 12:33