Why Do Matrix Expressions Often Involve A A^T in Factorization?

[MikeLowri123]

Hi All,

I often see this term when factorizing out a matrix from brackets

A(some other term)A^T

where I assume A A^T represents the square within the bracket term, can someone explain the reasoning behind expressions of this kind or point me in the correct direction

Many thanks

 

[micromass]

Can you give a concrete example?

 

[MikeLowri123]

For example when removing the L term from the variance in the attached equations, can you make this out?