How to interchange columns of a matrix?

Question

Suppose I have a matrix

M={{1,2,3},{4,5,6},{7,8,9}}//MatrixForm

What code do I write to interchange columns and make it into

{{2,3,1},{5,6,4},{8,9,7}}

The question mentioned here, Elegant operations on matrix rows and columns

does not solve the problem because, I am using //MatrixForm with the list, and it is not working for interchanging columns, while it works for interchanging rows !

@kglr it interchanges rows not columns. Program is not working for columns !!! — Chetan Waghela, May 29 '19 at 11:18
@MichaelE2 I tried methods of the question you posted, it is not working for columns. — Chetan Waghela, May 29 '19 at 11:24
It's there: m2 = m; m2[[All, {1, 3}]] = m2[[All, {3, 1}]] -- instead of {3, 1} --> {1, 3}, use the permutation of columns you want. (Note, it's the same as @kglr's comment above.) — Michael E2, May 29 '19 at 11:26
@MichaelE2 Yes I had tried it earlier. However, it did not work. Now, I removed the //MatrixForm from the list and it works ! I do not know the reason. — Chetan Waghela, May 29 '19 at 11:28
Yeah, MatrixForm does not work like some other "Forms": https://mathematica.stackexchange.com/questions/3098/why-does-matrixform-affect-calculations — Michael E2, May 29 '19 at 11:30
If M is defined with MatrixForm, maybe newM=M[[1,All,{2,3,1}]]? — user1066, May 29 '19 at 14:00

a20 · Answer 1 · 2019-05-29T13:02:53.187

0

There are several methods, but the quickest, general one that is easily adjusted for more complicated permutations, is probably:

M = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}
Map[{#[[2]],#[[3]],#[[1]]}&,M]

That is, you take every row of M, and create the list {#[[2]],#[[3]],#[1]}, where e.g. #[[2]] refers to the second element of the row that is being acted upon.

You can of course also solve this by simple matrix multiplication:

A = {{0,0,1},{1,0,0},{0,1,0}}

M.A then gives you your requested matrix.

edited May 29 '19 at 13:02

answered May 29 '19 at 11:13

a20

912
5
17

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Your Map hanges the rows not the columns I think! – Ulrich Neumann May 29 '19 at 11:14
It changes each row separately to the requested format. Try it, it gives the correct form. – a20 May 29 '19 at 11:15
You're right, but in the question I read " interchange columns" – Ulrich Neumann May 29 '19 at 11:17
@Ulrich Neumann Yes you are right I am not able to interchange columns. I tried a lot of things, maybe I am doing something wrong. – Chetan Waghela May 29 '19 at 11:21
@UlrichNeumann yes, and the columns will as a result of the above map function be interchanged. I do not see the issue? – a20 May 29 '19 at 11:25
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N is a protected symbol in Mathematica, you cannot assign values to it. – Roman May 29 '19 at 11:59

How to interchange columns of a matrix?

1 Answers1