The discussion revolves around the unique decomposition of a square matrix into symmetric and skew-symmetric components. The original poster presents a statement regarding an nxn matrix and seeks to prove the decomposition A = B + C, where B is symmetric and C is skew-symmetric.
The conversation is ongoing, with some participants providing guidance on manipulating the identified expressions. There is a recognition of the relationship between the components, but no consensus has been reached on the next steps or the overall proof.
Participants express confusion regarding the implications of their findings and the requirements for the proof, indicating a need for further clarification on the decomposition process.
mlarson9000 said:(A+A^T)is symmetric, (A-A^T)is skew symmetric, but adding them together produces 2A, not A. I'm not sure what to do with this information.
Dick said:That's not such a big problem. Divide each one by two.