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I have matrix and need to subtract another matrix element by element on each row. Something like this:

$$ \begin{pmatrix} x_{1} & x_{2}\\ x_{3} & x_{4}\\ \vdots & \vdots\\ x_{n-1} & x_{n}\\ \end{pmatrix} - \begin{pmatrix} y_{1} & y_{2}\\ \end{pmatrix} $$

So end result should be something like:

$$ \begin{pmatrix} x_{1} - y_{1} & x_{2} - y_{2}\\ x_{3} - y_{1} & x_{4} - y_{2}\\ \vdots & \vdots\\ x_{n-1} - y_{1} & x_{n} - y_{2}\\ \end{pmatrix} $$

How to do this? How to do this in Octave, Matlab?

Sorry for noob question. Also would be very kind if you pint me where to read about this.

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for loop is always a good start. – picakhu Nov 29 '11 at 22:12
    
'for loop' is done :), now need more. I found solution - bsxfun(@minus, X, Y).. – Mike Chaliy Nov 29 '11 at 22:16
    
@moderators, pls, close this topic, this mostly exact duplicate of the math.stackexchange.com/questions/5793/… – Mike Chaliy Nov 29 '11 at 22:18
    
How about x - repmat (y, [n 1]) ; – littleO 2 days ago
up vote 4 down vote accepted

With the current version (3.6) of Octave, simply subtracting will work

> a = [1 2; 3 4; 5 6; 7 8]
> b = [1 -1]
> a - b
ans =

   0   3
   2   5
   4   7
   6   9
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In Octave (3.4) this gives an error: a - b error: operator -: nonconformant arguments (op1 is 4x2, op2 is 1x2) – asmaier Oct 27 '13 at 19:15
    
This depends if the feature called "Automatic Broadcasting" is turned on or not. You can turn it off to make make sure your code is more compatible with Matlab if you want to. – mathreadler 2 days ago

Solution from Stackoveflow - http://stackoverflow.com/a/1773119/38975

bsxfun(@minus, X, y);
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This works also in Octave 3.4 – asmaier Oct 27 '13 at 19:23

The following is also a Kronecker product shortcut and is quite general: Suppose your $X,y_1,y_2$ is in the workspace, then

result = X - kron(ones(size(X,1),1),[y1 y2]);

gives you the ... result :)

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If your matrices are only two columns, here's a nasty way to do it:

>> a = [1 2; 3 4; 5 6; 7 8]
>> b = [1 -1]

>> [a(:,1)-b(1),a(:,2)-b(2)]
ans =

   0   3
   2   5
   4   7
   6   9

I suspect there's a better way though ...

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Another way to do it is by outer product:

> a = [1 2; 3 4; 5 6; 7 8]
> b = [1 -1]
> a - ones(4,1)*b

This easily gets nastier to express with outer products if you start having 3,4 or even more dimensions and want to replicate any subset of them though.

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