[Don Harlow, Joe Shaw, Pam Korda, Leigh Butler, Jennifer Liang]
When Mat went into the Red Door of Rhuidean, he asked for the holes in his memory to be filled [TSR: 24, Rhuidean, 281]. He ended up with more than he bargained for. The holes were filled with "historical" memories, memories from people who lived between the time of the Trolloc Wars and the time of Hawkwing. In every memory, he is a military man, and most of his memories are of fighting and battles:
"Slices of other men's lives packed his head now, thousands of them, sometimes only a few hours, sometimes years altogether though in patches, memories of courts and combats stretching for well over a thousand years, from long before the Trolloc Wars to the final battle of Artur Hawkwing's rise. All his now, or they might as well be." [LOC: 5, A Different Dance, 113]
There were essentially two theories offered for this:
Johannes Rydh reports that RJ answered this question in a post-WH Dromen & Demonen chat:
RJ: Mat's memories are NOT from his ancestors. He said [he wanted] to have the holes in his head filled but he did not specify exactly what he wanted them filled with and so he received scraps and bits and pieces of memories stolen from other men.
He explained the idea more fully in the interview included in the online version of COT's Prologue:
Q: Are all of Mat's memories from his past lives?
RJ: No, Mat's "old" memories are not from his past lives at all. The "sickness" he got from the Shadar Logoth dagger resulted in holes in his memory. He found whole stretches of his life that seemed to be missing. When he passed through the "doorframe" ter'angreal in Rhuidean, one of the things he said - not knowing that the rules here were different than in the other ter'angreal he had used - was that he wanted the holes in his memory filled up, meaning that he wanted to recover his own memories. In this place, however, it was not a matter of asking questions and receiving answers, but of striking bargains for what you want. What he received for that particular demand was memories gathered by the people on that side of the ter'angreal, memories from many men, all long dead, from many cultures. And since not everyone passing by has the nerve to journey through a ter'angreal to some other world, the memories he receieved were those of adventurers and soldiers and men of daring.
This corresponds with Cyndane's thought in WH about being held by the Aelfinn AND the Eelfinn, which implied that there must be some sort of connection between the Snaky place and the Foxy place. According to Moiraine in TSR, the AS who studied the Snake door in Tear said that the Snakes (the Aelfinn) feed on experiences and emotions - memories, in other words [TSR: 15, Into the Doorway, 179].
The Fox doorway may have been stuck in Rhuidean since the Breaking, but the Snake doorway was easily accessible and in regular use in Mayene and elsewhere during most of that time until the Tairens squirreled it away three hundred years ago [TSR: 6, Doorways, 95-96]. It's not unreasonable to suppose (and in fact it may even have been stated somewhere) that the Firsts of Mayene would let anyone who wanted to risk it go through the doorway.
Thus, the Foxes probably got the memories they gave Mat from the Snakes, who got them from the kind of guys willing to step through a mysterious doorway to another dimension just for the hell of it.
So that makes sense, at least as far as it goes. However, it does not explain why Mat had historical flashbacks of a military nature before he went to Rhuidean. (Consider the scene in TDR where he is Healed in the Tower [TDR: 19, Awakening, 167-168].) The COT interview also seems to contradict a statement RJ made to John Hamby at a post-TPOD signing: "Gender/soul rebirth, he said, is best illustrated by Mat and Birgitte."
The easiest (and most charitable) way to explain this discrepancy is to assume that it is not a discrepancy at all - that in fact, both theories are correct. In other words, Mat got most of his memories from the Foxes, who got them from the Snakes, who got them from other men, but Mat's pre-Rhuidean historical memories came from memories of earlier lives.
This is supported by the fact that Mat's pre-Rhuidean memories seem to concern Manetheren exclusively, while his later memories are from all over the place. Also recall Moiraine's talk of the "Old Blood" coming through in the descendants of Manetheren in TEOTW. Mat's Old Blood/racial memory tendencies could explain why the Snakes addressed him so ("Go to Rhuidean, son of battles!"). The Snakes' sending him to Rhuidean - where they may very well have known exactly what their Foxy buddies would smush into Mat's head - may simply have been a recognition of that archetype, maybe their way of fulfilling it or bringing it to its full potential.
There has been a lot of speculation that Mat is the reincarnation of an ancient king of Manetheren. However, there is nothing that really supports this theory. Though he does form the Band of the Red Hand near the end of TFOH, which was supposedly a band of heroes who went down defending Aemon himself, this suggests more that he was a guardian or advisor to the king than a king himself.
This was emphasized earlier on, in TSR. When Jasin Natael is singing a song about a battle at a river and how the enemy of Manetheren had mercy on the defeated Manetherenites, because they were so brave, etc. Mat remembers himself, as the king's advisor, being killed by that foe's treachery; and then he remembers himself, somebody else, seeing that foe, older and grayer, being killed in another battle somewhere else. [TSR: 37, Imre Stand, 424-425].
So it's very doubtful that Mat was Aemon, or any other king of Manetheren.
How did the Foxes get memories of people dying?
Mat comments in [COT: 3, A Fan of Colors, 141] that he hates remembering dying, and some people have wondered how the Foxes/Snakes got a memory from someone that clearly had to date from after that person had gone through the doorway ter'angreal.
As Jamie Bowden explains, however, time cannot be linear for the Finn, because otherwise they wouldn't be able to answer questions about your future. So clearly they get to rummage through your whole life, past and future, in one visit.
Mat's Theory
During a ride with Tuon, Mat becomes overwhelmed with the memories of another time and begins to speculate on how these memories were collected in the first place. [KOD 8: Dragon Eggs]
Maybe they created some sort of link to any human that visited them, a link that allowed them to copy all of a man's memories after that right up to the moment he died. In some of those memories from other men, he was white-haired, in some only a few years older than he really was, and everything in between, but there were none of childhood or growing up.
Later on his comments make it seem as if he believes the Finns might be seeing events through his eyes as he experiences them.
Does Mat have memories of being two people at once?
There is no mention of Mat having memories of being two different people at the same time. A common misconception is that the sequence of memories described above in [TSR: 37, Imre Stand, 424-425] indicates that Mat has memories of being two different people in the same battle.
This is not the case!
What is actually going on is that these are two different guys, at different times. In the earlier memory, Mat is an advisor to a king, and is killed through the treachery of the enemy. In the later memory, Mat recalls seeing that same enemy, then older and grayer , die in another battle someplace else. There is enough time between the two incidents for the enemy to age considerably, and thus obviously could not have taken place in the same battle.