Contents
A5
A = [1 5 -8 7;-2 0 6 5;1 2 2 1]; B = [1 1 2;-5 1 4; 2 1 0]; u = [0;1;0]; v = [1 1 1]; %(a) B*B; B'*B; B'*B'; B*B'; B*A; B'*A; A'*B; B*u; B'*u; A'*u; B*v'; B'*v'; A'*v'; %(b) v*A % auch A'*v' v*B % auch B'*v' B*v' % auch v*B' %(c) u'*A B*u %(d) v*u %(e) u*v %(f) v*A*(u'*A)'
ans =
0 7 0 13
ans =
-2 3 6
ans =
4
0
3
ans =
-2 0 6 5
ans =
1
1
1
ans =
1
ans =
0 0 0
1 1 1
0 0 0
ans =
65
A6
%a) %Size n=16; %Vektoren d = -2*ones(n,1); nd= ones(n-1,1); %Matrix D=diag(d ,0)+diag(nd ,-1)+diag(nd ,1); D(end,1)=1; D(1,end)=1; D %b) %Vektoren z=zeros(n-3,1); cr=[-2; 1; z;1]; %Matrix Db=toeplitz(cr) %c) m=8 %Vektor r=1:m; c=eye(m,1); %Matrizen G = toeplitz(c,r) format rat H = toeplitz(1./r)
D =
Columns 1 through 13
-2 1 0 0 0 0 0 0 0 0 0 0 0
1 -2 1 0 0 0 0 0 0 0 0 0 0
0 1 -2 1 0 0 0 0 0 0 0 0 0
0 0 1 -2 1 0 0 0 0 0 0 0 0
0 0 0 1 -2 1 0 0 0 0 0 0 0
0 0 0 0 1 -2 1 0 0 0 0 0 0
0 0 0 0 0 1 -2 1 0 0 0 0 0
0 0 0 0 0 0 1 -2 1 0 0 0 0
0 0 0 0 0 0 0 1 -2 1 0 0 0
0 0 0 0 0 0 0 0 1 -2 1 0 0
0 0 0 0 0 0 0 0 0 1 -2 1 0
0 0 0 0 0 0 0 0 0 0 1 -2 1
0 0 0 0 0 0 0 0 0 0 0 1 -2
0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
Columns 14 through 16
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
-2 1 0
1 -2 1
0 1 -2
Db =
Columns 1 through 13
-2 1 0 0 0 0 0 0 0 0 0 0 0
1 -2 1 0 0 0 0 0 0 0 0 0 0
0 1 -2 1 0 0 0 0 0 0 0 0 0
0 0 1 -2 1 0 0 0 0 0 0 0 0
0 0 0 1 -2 1 0 0 0 0 0 0 0
0 0 0 0 1 -2 1 0 0 0 0 0 0
0 0 0 0 0 1 -2 1 0 0 0 0 0
0 0 0 0 0 0 1 -2 1 0 0 0 0
0 0 0 0 0 0 0 1 -2 1 0 0 0
0 0 0 0 0 0 0 0 1 -2 1 0 0
0 0 0 0 0 0 0 0 0 1 -2 1 0
0 0 0 0 0 0 0 0 0 0 1 -2 1
0 0 0 0 0 0 0 0 0 0 0 1 -2
0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0 0
Columns 14 through 16
0 0 1
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
-2 1 0
1 -2 1
0 1 -2
m =
8
G =
1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7
0 0 1 2 3 4 5 6
0 0 0 1 2 3 4 5
0 0 0 0 1 2 3 4
0 0 0 0 0 1 2 3
0 0 0 0 0 0 1 2
0 0 0 0 0 0 0 1
H =
Columns 1 through 5
1 1/2 1/3 1/4 1/5
1/2 1 1/2 1/3 1/4
1/3 1/2 1 1/2 1/3
1/4 1/3 1/2 1 1/2
1/5 1/4 1/3 1/2 1
1/6 1/5 1/4 1/3 1/2
1/7 1/6 1/5 1/4 1/3
1/8 1/7 1/6 1/5 1/4
Columns 6 through 8
1/6 1/7 1/8
1/5 1/6 1/7
1/4 1/5 1/6
1/3 1/4 1/5
1/2 1/3 1/4
1 1/2 1/3
1/2 1 1/2
1/3 1/2 1
A7
Matrix
M = magic(1000); % Diagonalsummen d_sum = sum(diag(M)); d2_sum = sum(diag(flip(M))); s_sum = sum(M); % Spaltensummen z_sum = sum(M'); % Zeilensummen D_true=(d_sum == d2_sum); % 1 falls Diagonalen gleich, sonst 0. S_true=prod(s_sum == d_sum); % 1 falls Diag. = jeder Spaltensumme sonst 0. Z_true=prod(z_sum == d_sum); % 1 falls Diag. = jeder Zeilensumme sonst 0. ERG = D_true*S_true*Z_true % 1 falls alles erfüllt sonst 0.
ERG =
1
A8
n=8; A = toeplitz(0:n,0:-1:-n) B = A.*(A>=0) C = isprime(B) D = C.*B
A =
Columns 1 through 5
0 -1 -2 -3 -4
1 0 -1 -2 -3
2 1 0 -1 -2
3 2 1 0 -1
4 3 2 1 0
5 4 3 2 1
6 5 4 3 2
7 6 5 4 3
8 7 6 5 4
Columns 6 through 9
-5 -6 -7 -8
-4 -5 -6 -7
-3 -4 -5 -6
-2 -3 -4 -5
-1 -2 -3 -4
0 -1 -2 -3
1 0 -1 -2
2 1 0 -1
3 2 1 0
B =
Columns 1 through 5
0 0 0 0 0
1 0 0 0 0
2 1 0 0 0
3 2 1 0 0
4 3 2 1 0
5 4 3 2 1
6 5 4 3 2
7 6 5 4 3
8 7 6 5 4
Columns 6 through 9
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
2 1 0 0
3 2 1 0
C =
Columns 1 through 5
0 0 0 0 0
0 0 0 0 0
1 0 0 0 0
1 1 0 0 0
0 1 1 0 0
1 0 1 1 0
0 1 0 1 1
1 0 1 0 1
0 1 0 1 0
Columns 6 through 9
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
1 0 0 0
1 1 0 0
D =
Columns 1 through 5
0 0 0 0 0
0 0 0 0 0
2 0 0 0 0
3 2 0 0 0
0 3 2 0 0
5 0 3 2 0
0 5 0 3 2
7 0 5 0 3
0 7 0 5 0
Columns 6 through 9
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
2 0 0 0
3 2 0 0