I agree with the previous answer,
the fundamental thing you need to do is set up a server on linux to send the graphics over the network, and have client software on the Windows machine that will connect to the linux's server software which is pumping its graphics over the network.
But be aware if the linux machine has a nvidia graphics card or more specifically the software on the linux system uses the graphics card to render images that you are likely to have problems. With many of the free approaches to remote desktop for linux such as tightvnc, they will not push graphics from the graphics card over the network. This is also true for software that uses hardware accelerated OpenGL.
If your matlab (or whatever software) does everything at the prompt and just crunches numbers without doing graphics then you will probably be ok. But if you are doing high end matlab with graphics it might fail. And with any software if it uses OpenGL to display graphics that many of these free remote desktops for linux won't work.
You will get a specific OpenGL error when launching the software remotely, I forget the specific syntax at the moment.
I use NICE-DCV which is based on RealVNC, but it is not free. you can read their website for info.
Another option I know of is NxMachine from nomachine.com. You can test drive NxMachine for free to see if it suits your needs. I have experience with it and is rather easy and quick to get going with.
you can refer to en.wikipedia.org/wiki/VirtualGL and virtualgl.org/About/Introduction which gives a good description of the problem at large which is all about remote opengl.
This is for getting a fully functional remote desktop connection to linux.