Page 79 - A Guide to MATLAB for Beginners and Experienced Users

60 Chapter 4: Beyond the Basics

Solving Linear Systems
Suppose A is a nonsingular n × n matrix and b is a column vector of length n.
Then typing x=A\b numerically computes the unique solution to A*x=b.
Type help mldivide for more information.
If either A or b is symbolic rather than numeric, then x=A\b computes
the solution to A*x=b symbolically. To calculate a symbolic solution when
bothinputs are numeric, type x = sym(A)\b.

Calculating Eigenvalues and Eigenvectors
The eigenvalues of a square matrix A are calculated with eig(A). The com-
mand [U, R] = eig(A) calculates boththe eigenvalues and eigenvectors.
The eigenvalues are the diagonal elements of the diagonal matrix R, and the
columns of U are the eigenvectors. Here is an example illustrating the use of
eig:

>>A=[3-20;2-20;011];
>> eig (A)
ans =
1
-1
2
>> [U, R] = eig(A)
U=
0 -0.4082 -0.8165
0 -0.8165 -0.4082
1.0000 0.4082 -0.4082
R=
1 0 0
0 -1 0
0 0 2

The eigenvector in the first column of U corresponds to the eigenvalue
in the first column of R, and so on. These are numerical values for the
eigenpairs. To get symbolically calculated eigenpairs, type [U, R] =
eig(sym(A)).