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# constructing maps between modules

Let's start with a free module.

    i1 : R = ZZ/5[x,y,z];

    i2 : F = R^3

          3
    o2 = R

    o2 : R-module, free

A list of indices can be used to produce homomorphisms corresponding to the corresponding basis vectors.

    i3 : F_{0,1,2}

    o3 = | 1 0 0 |
         | 0 1 0 |
         | 0 0 1 |

                 3      3
    o3 : Matrix R  <-- R

    i4 : F_{0,1}

    o4 = | 1 0 |
         | 0 1 |
         | 0 0 |

                 3      2
    o4 : Matrix R  <-- R

    i5 : F_{1,2}

    o5 = | 0 0 |
         | 1 0 |
         | 0 1 |

                 3      2
    o5 : Matrix R  <-- R

Matrices are viewed as linear transformations.

    i6 : f = matrix{{x,y,z}}

    o6 = | x y z |

                 1      3
    o6 : Matrix R  <-- R

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_modules.m2:498:0.