Understanding Symmetric Matrix Properties: A Puzzling Example

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The discussion centers on the properties of symmetric matrices, specifically addressing a puzzling example related to matrix transposition. Participants express confusion over the order of operations in matrix multiplication, questioning why rT results in qTA instead of the expected order. There is also a request for clarification on the meaning of the symbols used, particularly regarding whether all superscripted T's represent matrices and if they are square matrices. Additionally, the dimensions of the matrices involved are questioned, highlighting the need for a deeper understanding of the example provided. The conversation emphasizes the complexities of symmetric matrices and the importance of notation in matrix operations.
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Homework Statement



http://img266.imageshack.us/img266/152/78148531ur5.png

Homework Equations



A is symmetric.

The Attempt at a Solution



First of all if you calculate rT you'll get qTA so why it the order reversed in the picture above? Moreover I don't see why it is zero.
 
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Can you go into more detail as to what those symbols mean? The superscripted T's clearly indicate that some of them are matrices, but are they all matrices? If so, then are they all square? If not, then how many rows and columns does each have?
 

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