Can a PSD Matrix Be Expressed as a Sum of Structurally Similar Matrices?

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SUMMARY

The discussion centers on the mathematical concept of expressing a positive semi-definite (PSD) matrix, denoted as A, as a sum of structurally similar matrices, specifically in the form A = B1 + B2 + ... + Bn. A participant suggests a simple solution where each Bi is defined as A/n. The conversation highlights the need for clarity in the question, indicating that further exploration of the properties and implications of such a decomposition may be necessary.

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peterlam
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Is it possible to express a n-by-n positive semi-definite matrix (A) in terms of a sum of n terms of something, i.e. A = B1+B2+...+Bn, where each Bi has similar structure?

Thanks!
 
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how about Bi = A/n

is there more to this question? its a litle smbiguous as is

also be sure to show your attempts
 

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