Yes, with a Home license, although the license terms restrict you to activation on one system at a time, you can transfer to a new system (a small number of times per year.) [Some people, including some Mathworks people, say that you can use a Home license on two systems at a time, but that does not agree with the R2015b license terms that were recently posted.]
I looked through the platform compatibility, and all the products you list there are supported on Linux. (I also confirmed that all of those toolboxes are available for Home license.)
So you should be good to go ahead.
