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These functions allow the multiplication of a normal (dense-representation)
vector by a sparse matrix.
V * A : Mtrx, MtrxSprs -> Mtrx
Given a dense-representation vector v or dense-representation matrix V
with c columns,
together with a sparse c x n matrix A, both over a ring R,
return the product v.A or V.A.
This is generally fast if
A is sparse and uses minimal memory.
MultiplyByTranspose(V, A) : Mtrx, MtrxSprs -> Mtrx
Given a dense-representation vector v or dense-representation
matrix V with c columns, together with a sparse n x c
matrix A, both over a ring R, return the product of v or V
by the transpose of A.
This is generally fast if A is sparse, and is much faster than
computing the transpose of A first. For example, if the
vector-matrix product v.A.Atr is required, then
the function call MultiplyByTranspose(v*A, A) should be
used to avoid forming the matrix A.Atr which is usually
dense. This product occurs in iterative algorithms such as Lanzcos.
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