How do you concatenate the rows of a matrix into a vector?

There are a couple of different ways you can collapse your matrix into a vector, depending upon how you want the contents of your matrix to fill that vector. Here are two examples, one using the function reshape (after first transposing the matrix) and one using the colon syntax (:):

>> M = [1 2 3; 4 5 6; 7 8 9];    % Sample matrix
>> vector = reshape(M.', [], 1)  % Collect the row contents into a column vector

vector =

     1
     2
     3
     4
     5
     6
     7
     8
     9

>> vector = M(:)  % Collect the column contents into a column vector

vector =

     1
     4
     7
     2
     5
     8
     3
     6
     9

A very important note in changing a matrix to a vector is that , MATLAB produce the output vector form the columns of the matrix, if you use A(:)

for example :

A = [1 2 3 ; 4 5 6]

B = A (:)

B = [1 4 2 5 3 6]

You can see the direction of changing in the following image.