MeatAxe: zte - Tensor Product

MeatAxe 2.4

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zte - Tensor Product

## Command Line

    zte [Options] A B Result

Options
  Standard options, see Standard Command Line Options

A
  Left factor.

B
  Right factor.

Result
  Result matrix

## Input Files

A
  Left factor (patrix or permutation).

B
  Right factor (patrix or permutation).

## Output Files

Result
  Result matrix

## Description

This program reads in two matrices or permutations and writes out their tensor (Kronecker) product. If A is an m×n matrix, and B is an m'×n' matrix, the result is an mm'×nn' matrix consisting of all possible products of entries from A and B. An example may make this clearer:

    $ zpr G1
    matrix field=17 nor=2 noc=3
    1 2 3
    1 1 0
    $ zpr G2
    matrix field=17 nor=2 noc=2
    2 0
    1 3
    $ zte G1 G2 P1
    $ zpr P1
    matrix field=17 nor=2 noc=6
    2 0 4 0 6 0
    1 3 2 6 3 9
    2 0 2 0 0 0
    1 3 1 3 0 0

If the input files contain permutations on n and n' points, respectively, the result is a permutation on nn' points, which describes the action of (A,B) on ordered pairs of points. This action is defined in the obvious way: (i,k) maps to (iA,kB). In the output, pairs are represented as numbers using the lexicographic ordering (1,1), ..., (1,n'), (2,1), ..., (n,n').