Matrix _ [...] -- select some columns of blocks

Matrix _ [...] -- select some columns of blocks

Synopsis:

Operator: _

Input:

an instance of class Matrix.

an instance of class Array.

Output:

an instance of class Matrix.

f_[i,j,k] -- extract some columns of blocks from a matrix f.

The source of f should be a direct sum, and the result is obtained by composition with the inclusion into the sum of the components numbered i, j, k. Free modules are regarded as direct sums.

i1 : f = map(ZZ^2 ++ ZZ^2, ZZ^2, {{1,2},{3,4},{5,6},{7,8}})



o1 = | 1 2 |

     | 3 4 |

     | 5 6 |

     | 7 8 |



              4        2

o1 : Matrix ZZ  <--- ZZ

i2 : f^[0]



o2 = | 1 2 |

     | 3 4 |



              2        2

o2 : Matrix ZZ  <--- ZZ

i3 : f^[1]



o3 = | 5 6 |

     | 7 8 |



              2        2

o3 : Matrix ZZ  <--- ZZ

i4 : f^[1,0]



o4 = | 5 6 |

     | 7 8 |

     | 1 2 |

     | 3 4 |



              4        2

o4 : Matrix ZZ  <--- ZZ

See also:

submatrix -- select part of a matrix

Module _ [...] -- get inclusion map into direct sum

Matrix ^ [...] -- select some rows of blocks

Code:

     -- ../../../Macaulay2/m2/matrix1.m2:658
     Matrix _ Array := Matrix => (f,v) -> f * (source f)_v