Allegory of the Caves Comparison

There are a couple of similarities between the Matrix and the allegory of the cave. One is that both those in the matrix and cave do not get a sense of what the TRUE world is. Their only understanding of the REAL world is through what the machines tell them (in the matrix) or what they see in the shadows (in the cave.) The other is the idea of true knowledge being difficult to grapple with. Many, when freed from the machines in the Matrix rebel and don't understand the reality of the world, some even want to go back (like Cypher who chose to return to the matrix in a deal for selling out Neo). Much like many people who leave the cave want to return because the sun (the truth) hurts they're eyes so they retreat back into the cave. Both suggest that many of us are incapable and unwanting to accept the true nature of the world, so we retreat into the cave, or deeper into the matrix.

Check out the website i linked in the source section.

They're are many other similarities depending on how deep you want to go with it. But these two should help you get started. Hope this is helpful. Also there are many website that address the philosophy of the Matrix, and several that deal specifically with how it relates to Plato's allegory of the cave.

A few differences could be things like that fact that the illusion of the cave is merely the natural mechanism for humans to understand the world given their experience, whereas the imprisonment of the people in the matrix is an oppresive system that necesarily needs it's subjects to stay in captivity. Other differences could stem from the idea that in the matrix, it is thought that eventually everyone could (and should) be freed from the matrix (as is the goal of neo and friends) whereas with the cave, it seams that there is no hegelian end to which all work towards, it is merely our warped perception of reality and a failure to see the true world, which is inherent in humans rather than inflicted upon them as it is in the matrix. Again, there are countless others, but these are the first to pop in to my head.