I want to learn some basic things using Matlab. I'd prefer a lightweight one in Linux. Is there any alternative?
There are several alternatives:
Octave is very similar to Matlab. For everyday use (without various toolboxes) Octave can be used as a transparent replacement.
SAGE is also great, but perhaps closer to Maple/Mathematica in functionality than Matlab.
Scilab has many features from Matlab/Mathematica.
If you like to program and has a use for the large number of extension libraries available in Python, I would definitely choose Python/Scipy/etc. If you need a simple monolithic package with linear algebra capabilities and syntax identical to Matlab then use Octave.
You can find many other alternatives here.