Matrix || Matrix -- join matrices vertically

Matrix || Matrix -- join matrices vertically

Synopsis:

Operator: || -- a binary operator

Input:

an instance of class Matrix.

Output:

an instance of class Matrix.

f||g -- yields the matrix obtained from matrices f and g by concatenating the columns.

i1 : R = ZZ[a..h];

i2 : p = matrix {{a,b},{c,d}}



o2 = | a b |

     | c d |



             2       2

o2 : Matrix R  <--- R

i3 : q = matrix {{e,f},{g,h}}



o3 = | e f |

     | g h |



             2       2

o3 : Matrix R  <--- R

i4 : p || q



o4 = | a b |

     | c d |

     | e f |

     | g h |



             4       2

o4 : Matrix R  <--- R

If one of the arguments is ring element or an integer, then it will be multiplied by a suitable identity matrix.

i5 : p || 33



o5 = {0} | a  b  |

     {0} | c  d  |

     {1} | 33 0  |

     {1} | 0  33 |



             4       2

o5 : Matrix R  <--- R

See also:

Matrix | Matrix -- join matrices horizontally

Code:

     -- ../../../Macaulay2/m2/matrix.m2:393
     Matrix || Matrix := Matrix => (f,g) -> concatRows(f,g)