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# reducedMatrix -- reduced matrix

- Usage:
    `reducedMatrix(Matrix)`
- Inputs:
  - M, a matrix,
- Outputs:
  - a matrix,

## Description

Returns a full rank matrix whose row space equals the row space of M.

    i1 : F = GF(4);

    i2 : n = 7;

    i3 : k = 3;

    i4 : L = apply(toList(1..k),j-> apply(toList(1..n),i-> random(F)));

    i5 : m=matrix(L)

    o5 = | 1 a+1 1   a a a+1 a |
         | 1 a+1 a+1 1 1 1   a |
         | 0 0   a+1 1 1 0   0 |

                 3      7
    o5 : Matrix F  <-- F

    i6 : reducedMatrix(m)

    o6 = | 0   0 a+1 1 1 0 0 |
         | 0   0 0   0 0 1 0 |
         | a+1 a 0   0 0 0 1 |

                 3      7
    o6 : Matrix F  <-- F

## Ways to use reducedMatrix:

- `reducedMatrix(Matrix)`

## For the programmer

The object reducedMatrix is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CodingTheory.m2:3268:0.