MATLAB is designed to work easily with matrices and vectors, and a number of methods exist to declare matrices and vectors. For example, an entire matrix can be entered on one line with rows separated by semicolons (;):
>> A=[1 3 2;-1 0 9]
A =
1 3 2
-1 0 9
The matrix can also be typed in row by row:
>> A=[ 1 3 2
-1 0 9]
A =
1 3 2
-1 0 9
Notice that the spacing used has no effect.
The transpose of a matrix can
be found using the quote symbol ('):
>> B=[0 3 ;3 4;6 6];
>> B'
ans =
0 3 6
3 4 6
The semicolon (;) at the end of a line stops MATLAB from
displaying the answer on the screen. Basic
matrix operations can be performed:
>> A+B ??? Error using ==> + Matrix dimensions must agree.
>> A+B'
ans =
1 6 8
2 4 15
>> A-B'
ans =
1 0 -4
-4 -4 3
>> A*B
ans =
21 27
54 51
>> inv(A*B) ans = -0.1318 0.0698 0.1395 -0.0543
There are other operations in MATLAB apart from the standard operations. Preceding an operation with a period (.) causes the operation to be applied on an element by element basis. For example, consider the following commands:
>> C=[0 -3 4; 5 -4 3]
C =
0 -3 4
5 -4 3
>> D=[1 1 9; -3 0 1]
D =
1 1 9
-3 0 1
>> C*D ??? Error using ==> * Inner matrix dimensions must agree.
>> C.*D
ans =
0 -3 36
-15 0 3
Here's another example of MATLAB's element by element procedure:
>> E=[1:4]
E =
1 2 3 4
>> E*E
??? Error using ==> *
Inner matrix dimensions must agree.
>> E^2 %E^2 is the same as E*E
??? Error using ==> ^
Matrix must be square.
>> E.^2
ans =
1 4 9 16
As demonstrated above, comments can be included in MATLAB with the % character. MATLAB ignores any characters after this symbol. It is good practice in any programming to include comments to explain details that are not immediately obvious.