method

determinant

v1_9_1_378 - Show latest stable - Class: Matrix

determinant()

public

Returns the determinant of the matrix. If the matrix is not square, the result is 0. This method’s algorism is Gaussian elimination method and using Numeric#quo(). Beware that using Float values, with their usual lack of precision, can affect the value returned by this method. Use Rational values or Matrix#det_e instead if this is important to you.

Matrix[[7,6], [3,9]].determinant
  => 63.0

# File lib/matrix.rb, line 674
  def determinant
    return 0 unless square?
    
    size = row_size - 1
    a = to_a
    
    det = 1
    k = 0
    loop do
      if (akk = a[k][k]) == 0
        i = k
        loop do
          return 0 if (i += 1) > size
          break unless a[i][k] == 0
        end
        a[i], a[k] = a[k], a[i]
        akk = a[k][k]
        det *= -1
      end

      for i in k + 1 .. size
        q = a[i][k].quo(akk)
        (k + 1).upto(size) do |j|
          a[i][j] -= a[k][j] * q
        end
      end
      det *= akk
      break unless (k += 1) <= size
    end
    det
  end

determinant

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