Elementary Arithmetic

A + B : MtrxSprs, MtrxSprs -> MtrxSprs
Given m x n sparse matrices A and B over a ring R, return A + B.
A - B : MtrxSprs, MtrxSprs -> MtrxSprs
Given m x n sparse matrices A and B over a ring R, return A - B.
A * B : MtrxSprs, MtrxSprs -> MtrxSprs
Given an m x n sparse matrix A over a ring R and an n x p sparse matrix B over R, return the m x p sparse matrix A.B over R.
x * A : RngElt, MtrxSprs -> MtrxSprs
A * x : MtrxSprs, RngElt -> MtrxSprs
Given an m x n sparse matrix A over a ring R and a ring element x coercible into R, return the scalar product x.A.
-A : MtrxSprs -> MtrxSprs
Given a sparse matrix A, return -A.
A ^-1 : MtrxSprs, RngIntElt -> MtrxSprs
Given a invertible square sparse matrix A over a ring R, return the inverse B of A so that A.B = B.A = 1. The coefficient ring R must be either a field, a Euclidean domain, or a ring with an exact division algorithm and having characteristic equal to zero or greater than m (this includes most commutative rings).
A ^ n : MtrxSprs, RngIntElt -> MtrxSprs
Given a square sparse matrix A over a ring R and an integer n, return the matrix power An. A0 is defined to be the identity matrix for any square matrix A (even if A is zero). If n is negative, A must be invertible (see the previous function), and the result is (A - 1) - n.
Transpose(A) : MtrxSprs -> MtrxSprs
Given an m x n sparse matrix A over a ring R, return the transpose of A, which is simply the n x m sparse matrix over R whose (i, j)-th entry is the (j, i)-th entry of A.
V2.28, 13 July 2023