Is there a word for 'opposite symmetry'? Watch

Lewk
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For example, if i have a matrix such as:

\[ \left( \begin{array}{cccc}

0 & 0 & 1 & 1 \\

1 & 0 & 0 & 0 \\

0 & 1 & 0 & 1 \\

0 & 1 & 0 & 0 \end{array} \right)\]

which is oppositely symmetrical along the leading diagonal, i.e. for a matrix with entries a[i,j] for row i and column j:
a[x,y] = \begin{cases}

0, & \text{if }a[y,x] = 1 \\

1, & \text{if }a[y,x] = 0

\end{cases}

Is there a technical name for this?

Any info much appreciated!
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Khallil
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(Original post by Lewk)
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I don't see any symmetry in the entries of that matrix. The only symmetrical matrix I've come across is the one below where the leading diagonal acts as a line of symmetry. As a result, it'll be equal to it's transpose so long as the original matrix is a square matrix with the same dimensions (n x n for instance):

\mathbf{M} = \begin{pmatrix} a & b & c \\ b & e & d \\ c & d & f \end{pmatrix} = \mathbf{M}^{T}

What do you mean by 'oppositely symmetrical'?
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Lewk
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(Original post by Khallil)
I don't see any symmetry in the entries of that matrix. The only symmetrical matrix I've come across is the one below where the leading diagonal acts as a line of symmetry. As a result, it'll be equal to it's transpose so long as the original matrix is a square matrix with the same dimensions (n x n for instance):

\mathbf{M} = \begin{pmatrix} a & b & c \\ b & e & d \\ c & d & f \end{pmatrix} = \mathbf{M}^{T}

What do you mean by 'oppositely symmetrical'?
sorry, i should've specified that the entries in the matrix i am looking at are either 1 or 0. The entries on either side of the diagonal are opposite, hence why i say 'oppositely symmetric'.
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BlueSam3
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Not that I'm aware of, no. I'm also not aware of anywhere this property is interesting. Where has it come up?
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TenMileTie
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contrantiasymmetry
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Shadow-X
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any girls on this thread?
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XxSophie01xX
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(Original post by Lewk)
For example, if i have a matrix such as:

\[ \left( \begin{array}{cccc}

0 & 0 & 1 & 1 \\

1 & 0 & 0 & 0 \\

0 & 1 & 0 & 1 \\

0 & 1 & 0 & 0 \end{array} \right)\]

which is oppositely symmetrical along the leading diagonal, i.e. for a matrix with entries a[i,j] for row i and column j:
a[x,y] = \begin{cases}

0, & \text{if }a[y,x] = 1 \\

1, & \text{if }a[y,x] = 0

\end{cases}

Is there a technical name for this?

Any info much appreciated!
I saw algebra and nearly self-combusted.
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davros
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(Original post by XxSophie01xX)
I saw algebra and nearly self-combusted.
Thousands of teenage girls die like this every year.

Help to end oppression and violence against women by signing an e-petition calling for Michael Gove to remove algebra from the school curriculum NOW!
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Lewk
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(Original post by BlueSam3)
Not that I'm aware of, no. I'm also not aware of anywhere this property is interesting. Where has it come up?
It's an adjacency matrix for a special type of digraph called a tournament, and it has this 'opposite symmetry' characteristic along the leading diagonal. I was just wondering if i could give a fancy technical term to it in my coursework.
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