input a matrix

input a matrix

Sections:

by its entries

by a function

identity matrix

by its entries

Using the function matrix is the most basic method for inputting a matrix. The entries are typed in by rows.

i1 : R = ZZ/5[s..z];

i2 : M = matrix {{ x^2+y, z^3}, {y^3-z,3*z-6*x-5*y}}



o2 = | x2+y z3    |

     | y3-z -x-2z |



             2       2

o2 : Matrix R  <--- R

by a function

The function map can be used to construct matrices.

i3 : G = map(R^3,3,(i,j)->R_i^j)



o3 = | 1 s s2 |

     | 1 t t2 |

     | 1 u u2 |



             3       3

o3 : Matrix R  <--- R

i4 : f = 3*s^2*v-t*u*v+s*t^2



        2     2

o4 = s*t  - 2s v - t*u*v



o4 : R

i5 : H = map(R^4,R^4,(i,j)->diff(R_j*R_i,f))



o5 = | v  2t 0  s  |

     | 2t 2s -v -u |

     | 0  -v 0  -t |

     | s  -u -t 0  |



             4       4

o5 : Matrix R  <--- R

identity matrix

The function id is used to form the identity matrix as a map from a module to itself.

i6 : id_(R^3)



o6 = | 1 0 0 |

     | 0 1 0 |

     | 0 0 1 |



             3       3

o6 : Matrix R  <--- R

i7 : id_(coker M)



o7 = | 1 0 |

     | 0 1 |



o7 : Matrix

The first example gives a 3x3 identity matrix formed in the ambient ring.