# Strange square matrix question

## Homework Statement

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

## 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?

BruceW
Homework Helper
Consider the defination of A, then, ##( n ## x ## n)^T = n ## x ## n ##
Implies (i,j) = (j,i)
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:
vela
Staff Emeritus