Vectors and Matrices
Last revision: January 11, 2017In this section we are going to cover some linear algebra
stuff. Octave
is especially well designed for those purposes.
Vectors are the most basic objects in Octave
. You already
know how to define some: V=1:5
yields V=(1,2,3,4,5)
. You can also
say:
But that’s a row vector. What if you want a column vector? There are two ways:
which means transpose (i.e.: convert rows into columns), or either you can do:
Either way it will work. You can cut vectors easily:
Matrices are not difficult to define either:
Of course, you can multiply a matrix with a column vector:
Solving a linear system is very easy. If your system is $A\vec x=\vec
b$, with $A$ a matrix and $\vec b$ a vector, then you can formally
write x = A \ b
, and that will solve the system by gaussian
reduction. An example, let’s solve the system:
So we write the matrix $A$ and the right hand side vector $\vec b$:
We can check easily that the solution is right:
as it should.
The special matrices are easy to find. For example, the identity, $I$, is called “eye” (yes, it’s someone’s idea of a joke):
Or the zero matrix:
Exercises
- Solve the following linear system of equations:
Check the solution!
- Find the 10-th power of the following matrix