Math 485 (Sect 2) -- Mathematical Modeling
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Section 1: MATLAB basics
Matrix notation:>> [1 2; 3 4; 5 6]gives
ans =
1 2
3 4
5 6
a 3x2 matrix.A vector is just an Nx1 (column) or 1xN matrix:
>> [1 2 3]
ans =
1 2 3
>> [1;2;3]
ans =
1
2
3
Operations on matrices include
- Addition:
>> [1 2; 3 4] + [1 3 ; 5 7] ans = 2 5 8 11 - Multiplication:
>> [1 2;3 4] * [-1 0;0 -1] ans = -1 -2 -3 -4 - We can multiply any size matrix, not just square ones:
>> [1 2;3 4] * [1 ; 1] ans = 3 7
Variables
You can store matrices and numbers in variables, like so:
>> a=[1 2; 3 4]
a =
1 2
3 4
>> b=[1 3 ; 5 7]
b =
1 3
5 7
>> a+b
ans =
2 5
8 11
Functions
MATLAB's built-in functions can apply to numbers or matrices (or vectors):
>> cos(pi)
ans =
-1
>> cos([-pi 0 pi])
ans =
-1 1 -1
Aside from basic functions like sin, cos, exp, MATLAB also
has a number of important operations on matrices.
- Eigenvalues:
>> a=[0 1; -1 -1] a = 0 1 -1 -1 >> eig(a) ans = -0.5000 + 0.8660i -0.5000 - 0.8660i - Eigenvalues and eigenvectors:
>> [v,e]=eig(a) v = 0.7071 0.7071 -0.3536 + 0.6124i -0.3536 - 0.6124i e = -0.5000 + 0.8660i 0 0 -0.5000 - 0.8660i - Inverting a matrix:
>> inv(a) ans = -1 -1 1 0 >> inv(a)*a ans = 1 0 0 1