Can We Solve Linear Algebra Problems at Extreme Scale and Low Precisions?
One interesting question is how to implement linear algebra for the case of binary variables x_i in {0,1} or x_i in {-1,0,+1} as opposed to having continuous variables. Of course, it will be somewhat different theory but the general properties should be analogous to those of standard linear algebra. For example, dot product should express the notion of orthogonality, there should be well defined distance etc. I am not sure that such a theory exists at all but if yes then I am curious if there exist implementations.