Matlab - Generacion de una matriz triagular inferior

% a      0      0               0 

% b      b-a    0               0

% c      c-b   (c-b)-(b-a)      0

% d      d-c   (d-c)-(c-b)      [(d-c)-(c-b)]-[(d-b)-(b-a)]

clear all

syms a b c d

C(:,1)=[a; b; c; d];

  for i=1:length(C)

     for j=i+1:length(C)

         C(j,i+1)=C(j,i)-C(j-1,i);

     end

 end

 C

%forma generica 

n=3; A=sym('A%d',[n,1]);

 for i=1:n

     for j=i+1:n

         A(j,i+1)=A(j,i)-A(j-1,i);

     end

 end

 A

%forma generica 

n=4; A=sym('A%d',[n,1]);

 for i=1:n

     for j=i+1:n

         A(j,i+1)=A(j,i)-A(j-1,i);

     end

 end

 A

>> matriz_simbolica

C =

[ a,     0,           0,                 0]

[ b, b - a,           0,                 0]

[ c, c - b, a - 2*b + c,                 0]

[ d, d - c, b - 2*c + d, 3*b - a - 3*c + d]

A =

[ A1,       0,              0]

[ A2, A2 - A1,              0]

[ A3, A3 - A2, A1 - 2*A2 + A3]

A =

[ A1,       0,              0,                     0]

[ A2, A2 - A1,              0,                     0]

[ A3, A3 - A2, A1 - 2*A2 + A3,                     0]

[ A4, A4 - A3, A2 - 2*A3 + A4, 3*A2 - A1 - 3*A3 + A4]

clc

clear all

v1=[2 5 16 45 46 708]';

m=zeros(numel(v1));

m(:,1)=v1;

for j=2:numel(v1)

    m(:,j)= [zeros(j-1,1);m(j:end,j-1)]-[zeros(j-1,1);m((j-1):(end-1),j-1)];

end

disp(m)

>> %forma numerica

clear all

n=4;

v=round(20*rand(n,1))

A(:,1)=v;

 for i=1:n

     for j=i+1:n

         A(j,i+1)=A(j,i)-A(j-1,i);

     end

 end

 A

v =

     8

    18

    16

    19

A =

     8     0     0     0

    18    10     0     0

    16    -2   -12     0

    19     3     5    17