# Tagged Questions

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### What do you call the following operations on a symmetric matrix?

Suppose we have a symmetric matrix of the following form, where the diagonal is always zero: \begin{array}{cccc} 0 & 1 & 1 & 0\\ 1 & 0 & 1 & 1\\ 1 & 1 & 0 & 0\\ 0 ...
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### permutations with a given condition!

What will be the number of permutations of n different things, taken r at a time,when p particular things is to be always included in each arrangement? I know the answer to this question but could not ...
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### If matrix $A$ is invertible, then there is a permutation of its rows leaving no-zeros on the diagonal

I need to prove this statement: "If $A$ invertible, then exist a permutation of its rows leaving no-zeros on the diagonal" and I tried using the definitos of invertible matrices and $LU$ ...
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### Permutations expressed as product of transpositions

There is a theorem that states that all permutations can be expressed as a product of transpositions. I have a couple of questions about this theorem: Does the product which is equal to the ...
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### Circular permutation of 20 person and 1 host.

20 were invited for a party, find the no ways in which 20 persons and the host can be seated around a circular table such that two particular person be seated on either side of host. Solution : ...
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### Are these two permutation matrices equivalent?

Definition: The permutation matrix $P_{ij}$ is the identity matrix with rows $i$ and $j$ reversed. When left-multiplied with another matrix, it exchanges rows $i$ and $j$. Am I right in thinking that ...
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### Span of Permutation Matrices

The set $P$ of $n \times n$ permutation matrices spans a subspace of dimension $(n-1)^2+1$ within, say, the $n \times n$ complex matrices. Is there another description of this space? In particular, ...
### How many $n\times m$ binary matrices are there, up to row and column permutations?
I'm interested in the number of binary matrices of a given size that are distinct with regard to row and column permutations. If $\sim$ is the equivalence relation on $n\times m$ binary matrices such ...