Matrix ++ Matrix -- direct sum of maps

Matrix ++ Matrix -- direct sum of maps

Synopsis:

Operator: ++ -- a binary operator, usually used for direct sum

Input:

an instance of class Matrix.

Output:

an instance of class Matrix.

f++g -- computes the direct sum of two maps between modules.

If an argument is a ring element or integer, it is promoted to a one by one matrix.

i1 : R = ZZ/101[a..c];

i2 : vars R ++ transpose vars R



o2 = {0}  | a b c 0 |

     {-1} | 0 0 0 a |

     {-1} | 0 0 0 b |

     {-1} | 0 0 0 c |



             4       4

o2 : Matrix R  <--- R

i3 : oo^[1]



o3 = {-1} | 0 0 0 a |

     {-1} | 0 0 0 b |

     {-1} | 0 0 0 c |



             3       4

o3 : Matrix R  <--- R

i4 : a++b++c



o4 = | a 0 0 |

     | 0 b 0 |

     | 0 0 c |



             3       3

o4 : Matrix R  <--- R

Selecting rows or columns of blocks:

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

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

See also:

directSum -- direct sum of modules or maps

Matrix | Matrix -- join matrices horizontally

Matrix || Matrix -- join matrices vertically