Strange square matrix question

  • Thread starter Jbreezy
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  • #1
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Homework Statement



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



Homework Equations





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?
 

Answers and Replies

  • #2
BruceW
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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.
 
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  • #3
vela
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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
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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.
 

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