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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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