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

AI Thread Summary
Matrix expressions often involve the term A A^T in factorization because it represents a symmetric positive semi-definite matrix, which is crucial in various mathematical applications. This form arises frequently in contexts like covariance matrices and projections, where A is a matrix of data points. The use of A A^T simplifies calculations and helps maintain the properties of the original matrix. A concrete example can be seen in the context of variance, where removing the L term leads to expressions that retain the necessary characteristics of the data. Understanding this concept is essential for effective matrix manipulation in linear algebra.
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
 
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Can you give a concrete example?
 
For example when removing the L term from the variance in the attached equations, can you make this out?
 

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