2.65 How to add the mean of each column of a matrix from each column?

Given \[ \left ( {\begin {array} {cc} 1 & 2 \\ 3 & 4 \end {array}} \right ) \] Find the mean of each column, and add this mean to each element of the corresponding column. The result should be

\[ \left ( {\begin {array} {cc} 3 & 5 \\ 5 & 7 \end {array}} \right ) \]

To subtract the mean, just replace Plus with Subtract below for Mathematica and replace @plus with @minus for Matlab. This shows that Matlab bsxfun is analogue to Mathematica’s MapThread.

Mathematica mat = {{1, 2}, {3, 4}} MapThread[Plus,{Transpose@mat, Mean[mat]}]

{{3, 5}, {5, 7}}

 

Matlab A=[1 2;3 4]; bsxfun(@plus, A, mean(A))

ans = 3 5 5 7

 

Maple Maple mean always return real value, even if exact is possible. A:=Matrix([[1,2],[3,4]]); for n from 1 to LinearAlgebra:-ColumnDimension(A) do A[..,n]:=A[..,n] +~ Statistics:-Mean(A[..,n]) od; A

\[ \left [\begin {array}{cc} 3.0 & 5.0 \\ 5.0 & 7.0 \end {array}\right ] \]