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Matrix || Matrix -- join matrices vertically

Synopsis

Usage:
f = g || h
Operator: ||
Inputs:
- g, a matrix, a m by n matrix.
- h, a matrix, a r by n matrix.
Outputs:
- f, a matrix, the m+r by n matrix, obtained from matrices g and h by concatenating the columns.

Description

i1 : R = ZZ[i..p];

i2 : g = matrix {{i,j},{k,l}}

o2 = | i j |
     | k l |

             2       2
o2 : Matrix R  <--- R

i3 : h = matrix {{m,n},{o,p}}

o3 = | m n |
     | o p |

             2       2
o3 : Matrix R  <--- R

i4 : f= g || h

o4 = | i j |
     | k l |
     | m n |
     | o p |

             4       2
o4 : Matrix R  <--- R

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

i5 : f || 33

o5 = {0} | i  j  |
     {0} | k  l  |
     {0} | m  n  |
     {0} | o  p  |
     {1} | 33 0  |
     {1} | 0  33 |

             6       2
o5 : Matrix R  <--- R

Caveat

It is assumed that the matrices g and h have the same Ring.

See also

Matrix | Matrix -- join matrices horizontally
ring(Matrix) -- Get the associated ring of an object