- #1
Mr Davis 97
- 1,462
- 44
Homework Statement
Same as title.
Homework Equations
The Attempt at a Solution
A defining property of a diagonal matrix is that ##A_{ij} = A_{ji} ~~\forall i,j \le n##. This means that ##((A)^{t})_{ji} = A_{ji}##. Therefore, we know that ##A^t = A##. This shows that a diagonal matrix is symmetric.
Is this an okay proof? Am I making too big of a leap in logic to start with ##A_{ij} = A_{ji} ~~\forall i,j \le n##? Or do I need to first prove that that statement is true for diagonal matrices?