clear

% scalar and vectors are matrices
a =  13;
assert(a(1,1) == 13);
    
v = [1 2 3]; % vectors are row vector by default
t = [4,5,6]; % can also use comma to separate values
assert(v(1,2) == 2);
assert(v(2) == 2);
t_col = t.'; % column vector given by transpose
assert(t_col(3, 1) == 6);

% complex transpose (adjoint matrix)
s = [1+1i 3-1i];
assert(all(s' == [1-1i 3+1i].'));

% size() finds the matrix dimensions of something
assert(all(size(a) == [1 1]));
assert(all(size(v) == [1 3]));
assert(all(size(v') == [3 1]));

% length() returns the largest dimension given by size()
assert(length(a) == 1);
assert(length(v) == 3);
assert(length(v.') == 3);

% isempty() is equivalent to length(X) == 0
assert(isempty(a) == false);
assert(isempty([]) == true);

% ndims() is equivalent so length(size(v))
% this proves that scalars and vectors are matrices
assert(ndims(a) == 2);
assert(ndims(v) == 2);
assert(ndims(v.') == 2);

% create a 3x3 matrix: rows separated by ;
M = [1 2 3; 4 5 6; 0 -1 -2];

assert(M(2, 3) == 6);
all(M' == [1 4 0; 2 5 -1; 3 6 -2]); % all operates on the first dimensions
                                    % returns [1 1 1];
% check all elements (i.e. all dimensions) by doing
assert(all(M.' == [1 4 0; 2 5 -1; 3 6 -2], 'all'));
% can be done better by doing
assert(isequal(M.', [1 4 0; 2 5 -1; 3 6 -2]));

% note: length on a matrix is not the number of elements
%       but the size of the max dimension
assert(length(M) == 3);

% numel() is equivalent to multiplying the entries given by size()
% returns the number of scalar elements
assert(numel(a) == 1);
assert(numel(v) == 3);
assert(numel(M) == 9);