O15-C083

> restart:with(linalg):
Warning, new definition for norm
Warning, new definition for trace
> a:=proc(n)
> local f;
> f:=(i,j)->if i=j then 0 else j fi;
> matrix(n,n,f);
> end;

  a := proc(n)
local f;
    f := proc(i, j)
        option operator, arrow;
            if i = j then 0 else j fi
        end;
    matrix(n, n, f)
end

> a(4);

                          [0    2    3    4]
                          [                ]
                          [1    0    3    4]
                          [                ]
                          [1    2    0    4]
                          [                ]
                          [1    2    3    0]

> res:=[]:for n from 2 to 5 do res:=[op(res),det(a(n))] od;

                             res := [-2]


                           res := [-2, 12]


                         res := [-2, 12, -72]


                      res := [-2, 12, -72, 480]

> eigenvects(a(2));

  [sqrt(2), 1, {[1, 1/2 sqrt(2)]}],

        [-sqrt(2), 1, {[1, - 1/2 sqrt(2)]}]

> for n from 3 to 5 do evalf(eigenvals(a(n))) od;

                            -9
         3.766435484 - .1 10   I, -2.483611621, -1.282823864


                             -3.525025248


                             -4.554110919

>