Patriot Signature 8 GB (2 x 4GB) PC2-6400 DDR2-800 SoDIMM Dual Channel Desktop Memory Kit - PSD28G800SK
Granted I've been a computer consultant for 40 years and have assembled my own computers since the mid-70s. It's cheaper in today's market to buy the core PC or laptop and then just do upgrades such as high end video boards, more robust power supplies, etcetera.
Let me tell you, it was a gamble that the above memory worked as there was nothing on Sony's site to give you a technical clue. Basically the only site I found that listed memory matched to my laptop was at crucial.com. However they wanted $229 per 4GM stick plus tax and shipping. So, without further ado, I started researching for a memory stick that appeared to match Crucial's. Well as shown above I found the kit on Amazon, which saved me money on the price as well as no taxes or shipping.
The memory arrived yesterday. I just removed the laptop battery and the one screw on the bottom of the laptop that covered the memory; removed the old memory and installed the new. Put the cover back on the memory, put the laptop battery back on and booted up the laptop.
After clicking on Computer and then right clicking to get to Properties, the laptop showed that it recognized the 8GB of RAM and all is well. Keep in mind that for this to be useful you must be running a 64 bit version of Windows (or whatever other 64 bit OS you might have).