How to insert a column into a matrix, the correct Mathematica way

Question

I think Mathematica is biased towards rows not columns.

Given a matrix, to insert a row seems to be easy, just use Insert[]

(a = {{1, 2, 3}, {4, 0, 8}, {7 , 8, 0}}) // MatrixForm

1   2    3
4   0    8
7   8    0

 row = {97, 98, 99};
(newa = Insert[a, row, 2]) // MatrixForm

1   2   3
97  98  99
4   0   8
7   8   0

But to insert a column, after some struggle, I found 2 ways, I show below, and would like to ask the experts here if they see a shorter and more direct way (Mathematica has so many commands, and I could have overlooked one that does this sort of thing in much direct way), as I think the methods I have now are still too complex for such a basic operation.

First method

Have to do double transpose:

a = {{1, 2, 3}, {4, 0, 8}, {7 , 8, 0}}
column = {97, 98, 99}
newa = Transpose[Insert[Transpose[a], column, 2]]

1   97  2   3
4   98  0   8
7   99  8   0

Second method

Use SparseArray, but need to watch out for index locations. Kinda awkward for doing this:

(SparseArray[{{i_, j_} :> column[[i]] /; j == 2, {i_, j_} :> a[[i, j]] /; j == 1, 
              {i_, j_} :> a[[i, j - 1]] /; j > 1}, {3, 4}]) // Normal

1   97  2   3
4   98  0   8
7   99  8   0

The question is: Is there a more functional way, that is little shorter than the above? I could ofcourse use one of the above, and wrap the whole thing with a function, say insertColumn[...] to make it easy to use. But wanted to see if there is an easier way to do this than what I have.

For reference, this is how I do this in Matlab:

EDU>> A=[1 2 3;4 0 8;7 8 0]
A =
     1     2     3
     4     0     8
     7     8     0

EDU>> column=[97 98 99]';

EDU>> B=[A(:,1) column A(:,2:end)]

B =
     1    97     2     3
     4    98     0     8
     7    99     8     0

@WReach The question you linked is a bit more narrowly formulated, the request there was to add the column at the end (although some solutions there were more general and suited also for this one). — Leonid Shifrin
This question is also similar. There Janus draws attention to the 'trick' of inserting a column of zeros (say) by the ArrayFlatten method as follows: ArrayFlatten@{{a[[All, ;; 1]], 0, a[[All, 2 ;; 3]]}} (It seems to me that a recent question has been treated a lot more harshly than this one as a 'possible duplicate') — 681234
@TomD I think one reason for questions not treated quite on equal grounds is that more people were aware of the previous one as a duplicate (e.g. I did not know that the subject of this one was discussed before in such a similar setting, and surely neither did Sjoerd). That's because lots of folks (myself included) joined mma SO tag relatively recently. OTOH, once the question gets momentum (answers, votes, comments, etc), it starts its own life and closing may no longer be a good option. — Leonid Shifrin

Leonid Shifrin Leonid Shifrin · Accepted Answer · 2011-09-24T07:30:35

Your double Transpose method seems fine. For very large matrices, this will be 2-3 times faster:

MapThread[Insert, {a, column, Table[2, {Length[column]}]}]

If you want to mimic your Matlab way, the closest is probably this:

ArrayFlatten[{{a[[All, ;; 1]], Transpose[{column}], a[[All, 2 ;;]]}}]

Keep in mind that insertions require making an entire copy of the matrix. So, if you plan to build a matrix this way, it is more efficient to preallocate the matrix (if you know its size) and do in-place modifications through Part instead.

How to insert a column into a matrix, the correct Mathematica way

First method

Second method

5 Answers