The Ilum Gray Yellow Matrix Shard Datacron is located in the Eastern Ice Shelf map on Ilum grants a Yellow Matrix Shard.
The closest Republic quick travel point is the Republic Waystation quick travel point and the closest taxi is the Republic Waystation Speeder speeder point, both in the middle of the map.
The closest Imperial quick travel point is the Imperial Outpost quick travel point and the closest taxi is the Imperial Base Camp Speeder speeder point, both where you load in to the planet.
The Ilum Yellow Matrix Shard is in the Imperial Base and is available to both Imperial and Republic players. Finding this datacron will give you a Yellow Matrix Shard which cna be used to create a low-level relic, and will unlock the Galactic History 86: The Empire’s Revenge codex.