Matrix || Matrix -- join matrices vertically

Synopsis

• Operator: ||

• Usage:

  f = g || h

• 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

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

See also

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