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# NCMatrix || NCMatrix -- Join NCMatrices vertically

- Operator: ||
- Usage:
    `L = M || N`
- Inputs:
  - M, an instance of the type NCMatrix,
  - N, an instance of the type NCMatrix,
- Outputs:
  - L, an instance of the type NCMatrix,

## Description

This command joins NCMatrices vertically.

    i1 : A = QQ{a,b,c,d}

    o1 = A

    o1 : NCPolynomialRing

    i2 : M = ncMatrix {{a,b,c,d},{b,c,d,a}}

    o2 = | a b c d |
         | b c d a |

    o2 : NCMatrix

    i3 : N = M || 2*M || -3*M

    o3 = | a    b    c    d    |
         | b    c    d    a    |
         | 2*a  2*b  2*c  2*d  |
         | 2*b  2*c  2*d  2*a  |
         | -3*a -3*b -3*c -3*d |
         | -3*b -3*c -3*d -3*a |

    o3 : NCMatrix

## Ways to use this method:

- NCMatrix || NCMatrix -- Join NCMatrices vertically

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NCAlgebra/NCAlgebraDoc.m2:896:0.