RE: Creating a symmetric matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg46860] RE: [mg46853] Creating a symmetric matrix*From*: "David Park" <djmp at earthlink.net>*Date*: Fri, 12 Mar 2004 02:02:45 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Mark, Here's one method. maketest[n_] := Module[{mat = IdentityMatrix[n], i}, Do[Part[mat, i] = PadLeft[Table[a[i, j], {j, i, n}], n], {i, 1, n}]; mat] (testmat = maketest[3]) // MatrixForm triangularToSymmetric[mat_?MatrixQ] /; Equal @@ Dimensions[mat] := Module[{workmat = mat + Transpose[mat], i}, Do[Part[workmat, i, i] = Part[mat, i, i], {i, 1, Length[workmat]}]; workmat] triangularToSymmetric[testmat] // MatrixForm I added the matrix to its transpose and then replaced the diagonal elements from the original matrix. I wish there were a way I could replace the diagonal elements all at once. I'm interested in seeing the other answers you will get. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Mark Coleman [mailto:mark at markscoleman.com] To: mathgroup at smc.vnet.net Greetings, How can I efficiently build a symmetric matrix from an upper triangular one, i.e., extract the upper triangular elements and insert them into the lower triangle in such a way as to make the resulting square matrix symmetric? Thanks, Mark