Computing with matrices and vectors

Matrices: Matrices in MATLAB

Computing with matrices and vectors

You can easily add matrices in MATLAB, subtract then, multiply them (also scalar multiplication) and exponentiate them. Examples illustrate this best.

>>  A = [1 2 3; 4 5 6]
A =
     1     2     3
     4     5     6
>> B = diag([1 2 3])
B =
     1     0     0
     0     2     0
     0     0     3
>> At = A'   % transposed of A
At =
     1     4
     2     5
     3     6
>> A*B    % matrix multiplication
ans =
     1     4     9
     4    10    18
>> A*At
ans =
    14    32
    32    77
>> At*A
ans =
    17    22    27
    22    29    36
    27    36    45
>> ans + B   % addition of matrices
ans =
    18    22    27
    22    31    36
    27    36    48
>> 3*A       % scalar multiplication
ans =
     3     6     9
    12    15    18
>> v = [1; 2; 3]
v =
     1
     2
     3
>> A*v       % matrix-vector multiplication
ans =
    14
    32
>> v'*A'     % vector-matrix multiplication
ans =
    14    32
>> B^3       % exponentiation:  B^3 = B*B*B
ans =
     1     0     0
     0     8     0
     0     0    27
>> B^(-1)    % inverse as power
ans =
    1.0000         0         0
         0    0.5000         0
         0         0    0.3333
>> A/B - A*B^(-1)  % division considered as multiplication with inverse
ans =
     0     0     0
     0     0     0
>> B\At - B^(-1)*At
ans =
     0     0
     0     0
     0     0

If you want to use addition, subtraction, multiplication and exponentiation in components of vector or matrix elements, then place a point before the operator. We give some examples.

Operations on matrix elements

>> A
A =
     1     2     3
     4     5     6
>> A .^ 2
ans =
     1     4     9
    16    25    36
>> A .* A
ans =
     1     4     9
    16    25    36
>> A ./ A
ans =
     1     1     1
     1     1     1