Matrix || Matrix -- join matrices vertically

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

If one of the arguments is a ring element or a number, 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.

Ways to use this method:

Matrix || Matrix -- join matrices vertically
Matrix || Number
Matrix || RingElement
Number || Matrix
RingElement || Matrix
RingElement || RingElement

The source of this document is in Macaulay2Doc/operators/concatenate.m2:80:0.

Matrix || Matrix -- join matrices vertically

Description

Caveat

See also

Ways to use this method: