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

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MikeLowri123
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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
 
For example when removing the L term from the variance in the attached equations, can you make this out?
 
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  • Two aligned equations: first line Var[x̂_t|t + L_t(x_t+1 - x̂_t+1|t) | y_0,...,y_T] equals second line L_t Var[(x_t+1 - x̂_t+1|t) | y_0,...,y_T] L_t^T.
    state2.png
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