You can do something like the following code. It assumes that each .mat file have a matrix named 'M'
files = dir('*.mat');
for i = 1:numel(files)
filename = files(i).name;
data = load(filename);
M = data.M;
v1 = M(:); % 1. Convert the contents of NxN matfile into N2X1 vector.
v2 = diag(M); % 2. Extract the diagonal elements from the mat file and save into another row vector
v3 = M(1,:); % 3. Extract the first row of the mat file and store into another vector.
save(filename, 'M', 'v1', 'v2', 'v3')
end
