Sketching as a Tool for Numerical Linear Algebra
... The most glaring omission from the above algorithm is which random familes of matrices S will make this procedure work, and for what values of r. Perhaps one of the simplest arguments is the following. Suppose r = Θ(d/ε2 ) and S is a r × n matrix of i.i.d. normal random variables with mean zero and ...
... The most glaring omission from the above algorithm is which random familes of matrices S will make this procedure work, and for what values of r. Perhaps one of the simplest arguments is the following. Suppose r = Θ(d/ε2 ) and S is a r × n matrix of i.i.d. normal random variables with mean zero and ...
Complex vector spaces, duals, and duels: Fun
... Thus, we can perhaps say (in our incorrigibly unrigorous way) that while R2 ∼ = C is true, it doesn’t capture all the structure of C, and in fact that (R2 , J) ∼ = (C, i) is better, whatever it means. In fact, it doesn’t mean much. All we really have is C, a (very trivial!) vector space over the com ...
... Thus, we can perhaps say (in our incorrigibly unrigorous way) that while R2 ∼ = C is true, it doesn’t capture all the structure of C, and in fact that (R2 , J) ∼ = (C, i) is better, whatever it means. In fact, it doesn’t mean much. All we really have is C, a (very trivial!) vector space over the com ...