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# Submitted by M. Edward (Ed) Borasky

require 'mathn' # also brings in matrix, rational and complex

# return a Hilbert matrix of given dimension

def hilbert(dimension)

  rows = Array.new

  (1..dimension).each do |i|

    row = Array.new

    (1..dimension).each do |j|

      row.push(1/(i + j - 1))

    end

    rows.push(row)

  end

  return(Matrix.rows(rows))

end

def run_hilbert(dimension)

  m = hilbert(dimension)

  print "Hilbert matrix of dimension #{dimension} times its inverse = identity? "

  k = m * m.inv

  print "#{k==Matrix.I(dimension)}\n"

  m = nil # for the garbage collector

  k = nil

end

a = []

50_000_000.times { a << 1}

[10, 20].each do |n|

  run_hilbert(n)

end