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Given m x n matrices A and B over a ring R, return A + B.
Given m x n matrices A and B over a ring R, return A - B.
Given an m x n matrix A over a ring R and an n x p matrix
B over R, return the m x p matrix A.B over R.
This function attempts to preserve the maximal amount of information in
the choice of parent for the product. For example, if A and B are both
square and have the same matrix algebra M as parent, then the product will
also have M as parent. Similarly, if the parents of A and B are
R-matrix spaces such that the codomain of B equals the domain A,
then the product will have domain equal to that of A and codomain
equal to that of B.
A * x : Mtrx, RngElt -> Mtrx
Given an m x n matrix A over a ring R and a ring element
x coercible into R, return the scalar product x.A.
Given a matrix A, return -A.
Given a invertible square 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).
Given a square 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.
Given an m x n matrix A over a ring R, return the
transpose of A, which is simply the n x m matrix over R
whose (i, j)-th entry is the (j, i)-th entry of A.
Given a matrix A over a ring R, a scalar s coercible into R,
and a matrix B over R with the same shape as A, return A + s.B.
This is generally quicker than the call A + s*B.
Given a matrix A over a ring R, a scalar s coercible into R,
and a matrix B over R with the same shape as A, set A to
A + s.B. This is generally quicker than the statement
A := A + s*B;.
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013