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Construction of a Matrix
Construction of a Matrix
M ! Q : ModMatRng, [RngElt] -> ModMatRngElt
Given the matrix bimodule M over the ring R, and the sequence
Q = [a_(11), ..., a_(1n), a_(21), ..., a_(2n), ..., a_(m1), ..., a_(mn)]
whose terms are elements of the ring R, construct the m x n matrix
[ a_11 a_12 ... a_1n ]
[ a_21 a_22 ... a_2n ]
[ ... ]
[ ... ]
[ a_m1 a_m2 ... a_mn ]
as an element of M. In the context of the sub or quo
constructors the coercion clause M ! may be omitted.
Example HMod_Matrix (H43E6)
We create the 4 x 4 Hilbert matrix h4 as an element of
the endomorphism ring of the 4-dimensional vector space over the rational
field.
> Q := RationalField();
> R4 := RModule(Q, 4);
> M := EndomorphismAlgebra(R4);
> h4 := M ! [ 1/i : i in [1 .. 16 ] ];
> h4;
[ 1 1/2 1/3 1/4]
[ 1/5 1/6 1/7 1/8]
[ 1/9 1/10 1/11 1/12]
[1/13 1/14 1/15 1/16]
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