The matrix multiplication PEP is actually titled "A dedicated infix operator for matrix multiplication", and that's (broadly) the only thing that it provides. Here's the arguments for why the operator should exist: https://www.python.org/dev/peps/pep-0465/#why-should-matrix-...
numpy and other libraries might/has/will implement the matrix multiplication infix operator for their array and matrix data types.
http://legacy.python.org/dev/peps/pep-0465/#id24
Implementing __matmul__, __rmatmul__ and __imatmul__ will allow you to apply this operator to any given class. In that light, you could subclass the numpy matrix class yourself and simply apply these.
As for whether these will be applied to Python lists, my speculation is: I doubt it. Its possibly the most commonly used data structure, and I doubt they would add the overhead of another set of methods on each instance.
It wouldn't incur any overhead, don't know why you'd think it would. Each method of any object only needs to be stored once, not again for every instance. The overhead comes from pointers and data fields such as the length.
Unless I'm grossly mistaken, Python methods add basically no per-instance overhead (they add per-class overhead.)
I tried hard to think of ways to (ab)use '@', and this XML example and perhaps some sort of messaging API were the only two I could come up with where there was a natural domain-specific mapping.
One of the advantages of keeping '@' at the same precedence level and ordering as '*', '/', '%', and '//' is that it doesn't really offer much in the way of new use. If someone uses '@' for something very unlike matrix multiplication, then they could already use any of the other 4 symbols that way.
So I don't think @ ends up as an attractive nuisance.
If you mean node[x] returns node.attrib.get(x) when x is a string, and the nth-child when x is an integer, then I think that puts too much complexity into the API.
If you mean stay with the existing node.attrib dict-like API, then node@name is a simple shortcut for node.attrib.get(name), but it's 1) more aligned with CSS/XSL '@' notation for attribute syntax, and 2) faster in CPython.
(Just realized that '/' and '//' also make sense in that context. node / "abc" / "xyz" @ "p" would be the child "abc"'s child "xyz"'s attribute "p". Perhaps my proposal is a bad idea because it might suggest that these other forms are allowed.)