compute determinant of a matrix

Question

I'm trying to compute determinant of a matrix in JS. I used algorithm from http://www.sanfoundry.com/java-program-compute-determinant-matrix/ but I lost my mind on the last condition. I just do not understand. Can you help me?

This is how looks like my code right now. In another function I create an empty 2d array and then copy it to det function. Next I retrieve values from html and then trying to compute determinant of a matrix. The first 2 cases are simple but I have a problem with the last one. I couldn't find working example in JS.

function det() {
  var det = 0;
  var array1 = array.slice();

  for (i = 0; i < array1.length; i++) {

    for (j = 0; j < array1[i].length; j++) {
      array1[i][j] = parseInt(document.getElementById("element" + (i + 1) + (j + 1)).value, 10);
    }

  }

  if (array1.length == 1) {
    det = array1[0][0];
  } else if (array1.length == 2) {
    det = (array1[0][0] * array1[1][1]) - (array1[1][0] * array1[0][1]);
  } else {

  }

}

in the last condition , you create a sub matrix which is array1 deleting the row and column at a0j where j is from 0 to N, you multiply a0j with det(subarray) and the sum of the products is the final determinant , that is the definition of determinant, the code written before the recursive call is just filling the subarray that's all — niceman

Yevgen Gorbunkov Yevgen Gorbunkov · Accepted Answer · 2019-08-28T15:50:01

I may suggest my solution, based on recursive algorithm, which takes only few lines of code and, I guess, will suit most of practical applications:

const determinant = m => 
  m.length == 1 ?
  m[0][0] :
  m.length == 2 ? 
  m[0][0]*m[1][1]-m[0][1]*m[1][0] :
  m[0].reduce((r,e,i) => 
    r+(-1)**(i+2)*e*determinant(m.slice(1).map(c => 
      c.filter((_,j) => i != j))),0)

const test1 = [[3]]                      // 3
const test2 = [[3,-2],[7,4]]             // 26
const test3 = [[1,3,7],[2,-1,4],[5,0,2]] // 81

console.log(determinant(test1))
console.log(determinant(test2))
console.log(determinant(test3))

.as-console-wrapper {min-height: 100%}

compute determinant of a matrix

2 Answers