Ok, I want to do the following to me it seems like a good idea so if there's no way to do what I'm asking, I'm sure there's a reasonable alternative.
Anyways, I have a sparse matrix. It's pretty big and mostly empty. I have a class called MatrixNode that's basically a wrapper around each of the cells in the matrix. Through it you can get and set the value of that cell. It also has Up, Down, Left and Right properties that return a new MatrixNode that points to the corresponding cell.
Now, since the matrix is mostly empty, having a live node for each cell, including the empty ones, is an unacceptable memory overhead. The other solution is to make new instances of MatrixNode every time a node is requested. This will make sure that only the needed nodes are kept in the memory and the rest will be collected. What I don't like about it is that a new object has to be created every time. I'm scared about it being too slow.
So here's what I've come up with. Have a dictionary of weak references to nodes. When a node is requested, if it doesn't exist, the dictionary creates it and stores it as a weak reference. If the node does already exist (probably referenced somewhere), it just returns it. Then, if the node doesn't have any live references left, instead of it being collected, I want to store it in a pool. Later, when a new node is needed, I want to first check if the pool is empty and only make a new node if there isn't one already available that can just have it's data swapped out.
Can this be done? A better question would be, does .NET already do this for me? Am I right in worrying about the performance of creating single use objects in large numbers?
Instead of guessing, you should make a performance test to see if there are any issues at all. You may be surprised to know that managed memory allocation can often outperform explicit allocation because your code doesn't have to pay for deallocation when your data goes out of scope.
Performance may become an issue only when you are allocating new objects so frequently that the garbage collector has no chance to collect them.
That said, there are sparse array implementations in C# already, like Math.NET and MetaNumerics. These libraries are already optimized for performance and will probably avoid performance issues you will run into if you start your implementation from stratch
An SO search for c# and sparse-matrix will return many related questions, including answers pointing to commercial libraries like ILNumerics (has a community edition), NMath and Extreme Optimization's libraries