php - How to multiply each element of N vectors to each other N^N times -

the problem have multiply each element of n vectors each other. example, if there 2 vectors name x,y. each has 3 elements. such x={x1,x2,x3} , y={y1,y2,y3} . multiplication following

m1={x1*y1}, m2={x1*y2}, m3={x1*y3}, m4={x2*y1}, m5={x2*y2}, m6={x2*y3}, m7={x3*y1}, m8={x3*y2}, m9={x4*y3} 

i can using 2 'for' loops. problem number of vector variable. can x,y,z or x,y or w,x,y,z. how can multiply them? there mathematical name of operation.

one of idea consider vectors 1 matrix.

here solution problem. syntax may different or depends on programming language using. store first element , perform multiplication of upcoming arrays. each , every element of arrays being multiplied 1 one.

<?php function multiplyvector($a=array(),$b) {     $count_a = count($a);     $count_b = count($b);      if($count_a)     {         for($i=0;$i<$count_a;$i++)         {             for($j=0;$j<$count_b;$j++)             {                 $result[] = $a[$i] * $b[$j];             }         }     }     else     {         $result = $b;     }      return $result; }  $x = [ 1, 2, 3 ];  $y = [ 7, 8, 9, 10 ];  $z = [ 10, 20, 50]; // add multiple array $main $main = [ $x, $y, $z ];  $result = array();  foreach($main $m) {     $result = multiplyvector($result,$m); }   echo "<pre>";print_r($result);die; 

and result here.

array (     [0] => 70     [1] => 140     [2] => 350     [3] => 80     [4] => 160     [5] => 400     [6] => 90     [7] => 180     [8] => 450     [9] => 100     [10] => 200     [11] => 500     [12] => 140     [13] => 280     [14] => 700     [15] => 160     [16] => 320     [17] => 800     [18] => 180     [19] => 360     [20] => 900     [21] => 200     [22] => 400     [23] => 1000     [24] => 210     [25] => 420     [26] => 1050     [27] => 240     [28] => 480     [29] => 1200     [30] => 270     [31] => 540     [32] => 1350     [33] => 300     [34] => 600     [35] => 1500 )