MATRICES

Entering matrices into Matlab is the same as entering a vector, except each row of elements is separated by a semicolon (;) or a return:

B = [1 2 3 4;5 6 7 8;9 10 11 12]

B =
   1  2  3  4
   5  6  7  8
   9  10   11   12

B = [ 1  2  3  4
        5   6  7   8
        9  10  11  12]

B =
   1  2  3  4
   5  6  7  8
   9  10  11  12
Matrices in Matlab can be manipulated in many ways. For one, you can find the transpose of a matrix using the apostrophe key:

C = B'

C =
    1   5    9
    2   6   10
    3   7   11
    4   8    12

Now you can multiply the two matrices B and C together. Remember that order matters when multiplying matrices.

D = B * C

D =
    30      70    110
    70     174   278
    110   278   446

D = C * B

D =
   107   122    137   152
   122   140   158    176
   137    158   179   200
   152    176   200   224
Another option for matrix manipulation is that you can multiply the corresponding elements of two matrices using the .* operator (the matrices must be the same size to do this).

E = [1 2;3 4]
F = [2 3;4 5]
G = E .* F

E =
   1    2
   3    4

F =
   2    3
   4    5

G =
   2     6
   12   20
If you have a square matrix, like E, you can also multiply it by itself as many times as you like by raising it to a given power.

E^3

ans =
     37    54
     81    118
If wanted to cube each element in the matrix, just use the element-by-element cubing.

E.^3

ans =
     1      8
     27   64
You can also find the inverse of a matrix:

X = inv(E)

X =
    -2.0000      1.0000
     1.5000     -0.5000
or its eigenvalues:

eig(E)

ans =
      -0.3723
       5.3723
There is even a function to find the coefficients of the characteristic polynomial of a matrix. The "poly" function creates a vector that includes the coefficients of the characteristic polynomial.

p = poly(E)

p =
   1.0000    -5.0000    -2.0000

Remember that the eigenvalues of a matrix are the same as the roots of its characteristic polynomial:

roots(p)

ans =
      5.3723
     -0.3723