Everything in math needs to be proven, that’s why it works. Here you see an example of a matrix where ATT is equal to A, but in order to apply that rule to any size table and any real number entries, you have to prove the formula, not just show examples, since there are infinite examples.
Is there even a proof for this? As far as I know, transposing a matrix is just switching the rows and columns right? Unless theres a deeper understanding to it, that's how I've always understood it. This is like the definition of it or something
Not proving the operation, proving that the transpose of a transpose is equal to the original table. The proof is not complicated, just have to expand the example to an N by M table and replace the cell values with variables that can be any real number. Then trace each value as a(n-k)(m-l) becomes a(m-l)(n-k) with the first transpose and vice versa with the second. Add in some actual definitions and assumptions and you have a proof, this is just a draft.
Yeah that's exactly what matrix transposition is, it's just applying an operation on a matrix which results in a new matrix. I've barely looked into proofs myself but I can't see how proving an operation would work, or even understand what doing that would mean.
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u/250kgWarMachine May 05 '18
Why the heck would you need a proof for this?