Hence there's some permutation of $A$ that does not appear in our list of all $RAC$ matrices.īTW, just to close this out: for $1 \times 1$ matrices, the answer is "yes, all permutations can in fact be realized by row and column permutations." I suspect you knew that. So the number of possible results of applying row- and col-permutations to $A$ is smaller than the number of possible permutations of the elements of $A$. &< \\īecause $2n \le n^2$ for $n \ge 2$, and factorial is an increasing function on the positive integers. Going back to the matrix A would entail multiplying again from the left by P 13: P 13 P 13 A ( P 13 P 13) A I A because every elementary permutation matrix (single transposition of rows) is its inverse: P P 1 or P 2 I. Where $R$ and $C$ each range independently over all $n!$ permutation matrices, we get at most $(n!)^2$ possible results. The permutation matrix is applied to the left. If we consider all expressions of the form T Theme Copy A -1 -1 1 1 -1 0 -3 0 1 1 0 0 B perms (A) Sign in to comment. I use below codes, it gives irrevalent result. But I couldn't figure out how to make on MATLAB. So I need to find permutation matrix for A (sc). There are $n!$ row-permutations of $A$ (generated by premultiplication by various permutation matrices), and $n!$ col-permutations of $A$ (generated by post-multiplication by permutation matrices). Some step of works wanted to find permuation matrix. B permute(A,dimorder) rearranges the dimensions of an array in the order specified by the vector dimorder. We can easily do this using permute in MATLAB, and Ill show you how to do that later. Since your matrix is 4x4, there are 6 values in the lower triangle excluding the diagonal. Matrix P has the same data type as v, and it has n rows and n columns. Since the permuted matrices are all symmetric, you really only need to permute the lower (or upper) triangle of the matrix, excluding the diagonal, and then reflect the values. Each row of P contains a different permutation of the n elements in v. Then there are $(n^2)!$ distinct permutations of $A$. P perms (v) returns a matrix containing all permutations of the elements of vector v in reverse lexicographic order. $$P_,$ would swap the columns $1$ and $3.Suppose the entries in the $n \times n$ matrix $A$ are all distinct. To access this command we just need to pass the order. If we want to exchange rows $n$ and $m,$ we need to swap the corresponding rows of the $I$ matrix: If $m=3$ and $n=1,$ The Dulmage-Mendelsohn decomposition (dmperm in MATLAB) can be used to do this for symmetric matrices (or just turn your non-symmetric matrix into a matrix of 0's and 1's with 1's replacing all non-zero entries in the original matrix.) Share Cite Follow answered at 3:58 Brian Borchers 10. Permute command in Permute Matlab is used to rearrange the elements within a multidimensional array. $IA,$ with $I$ being the identity matrix, selects every row of $A$ and leaves it in its place. Matrix Operations Description The Permute Matrix block reorders the rows or columns of an M-by-Ninput matrix Aas specified by indexing input P. function I, PMat permutationFromTo (A,B) ,IA sort (A) ,IB sort (B) I (IB) IA PMat (:,I) eye (length (A)) You can use it via: A rand (10,1) B A (randperm (10)) I, PMat permutationFromTo (A,B) // All the following three lines will output the vector B.
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