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#
# 4003.m
#
# (c) 2020 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
A = [
-13, 5, -29, 29;
-27, 11, -51, 51;
-3, 1, -2, 5;
-6, 2, -10, 13
];
eig(A)
lambda = 3
B = A - lambda*eye(4)
rref(B)
D = B*B*B*B
lambda = 2
B = A - lambda*eye(4)
rref(B)
D = B*B*B*B
b1 = [0;0;1;1]
b2 = [1;0;0;0]
b3 = [0;1;0;0]
b4 = [0;0;1;2]
T = zeros(4,4);
T(:,1) = b1;
T(:,2) = b2;
T(:,3) = b3;
T(:,4) = b4;
AA = inverse(T)*A*T
A1 = AA(2:4,2:4)
B1 = A1 - 2*eye(3)
B1 * B1
B1 * B1 * B1
c30 = [ 0; 1; 3; 1 ]
c3 = T*c30
lambda=2
B=A-lambda*eye(4)
c2=B*c3
c1=B*c2
T = zeros(4,4);
T(:,1) = [0;0;1;1]
T(:,2) = c1;
T(:,3) = c2;
T(:,4) = c3
det(T)
inverse(T)
det(T)*inverse(T)
inverse(T)*A*T
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