Strange square matrix question

1. Aug 17, 2013

Jbreezy

1. The problem statement, all variables and given/known data

Show that for a square matrix the (i,j) entry is equlivant to the (j,i) entry in a symmetric matrix.

2. Relevant equations

3. The attempt at a solution

I just felt this question was weird. They don't give the answers so I'm looking for confirmation.

I guess you could just do
$A = n$ x $n$
If symmetric
$A = A^T$
Consider the defination of A, then, $( n$ x $n)^T = n$ x $n$
Implies (i,j) = (j,i)

I don't know maybe this way?

2. Aug 17, 2013

BruceW

what does n x n mean? just the dimensions of the matrix? So, you've shown the transposed matrix has the same dimensions as the original one, but I don't see how this implies (i,j)=(j,i)... Are you familiar with index notation? And how the transpose of a matrix looks in index notation?

edit: uhhhh... you're right, it is a strange question. It seems to be pretty much asking you to just write down the definition. But I think your teacher/professor would be happier if you said something about index notation of matrices.

Last edited: Aug 17, 2013
3. Aug 17, 2013

vela

Staff Emeritus
You need to show that $A=A^T$ implies $a_{ij} = a_{ji}$. Those are two different statements. Start by considering what exactly it means to say that $A=A^T$.

4. Aug 17, 2013

Jbreezy

Oh yeah I guess that would be better. I just kind of fudged it. I know index notation.
Thanks dude. It is a dumb question.