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| author | Andreas Müller <andreas.mueller@othello.ch> | 2021-01-18 21:01:26 +0100 |
|---|---|---|
| committer | Andreas Müller <andreas.mueller@othello.ch> | 2021-01-18 21:01:26 +0100 |
| commit | 812a80acf52275699afb285db46aa76be03006c2 (patch) | |
| tree | d603bf9c54cd29909551d1cb7f5fd7b66c64ca4e /buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m | |
| parent | neue Sachen zur linearen Algebra (diff) | |
| download | SeminarMatrizen-812a80acf52275699afb285db46aa76be03006c2.tar.gz SeminarMatrizen-812a80acf52275699afb285db46aa76be03006c2.zip | |
add more stuff about spectral radius
Diffstat (limited to 'buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m')
| -rw-r--r-- | buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m | 66 |
1 files changed, 66 insertions, 0 deletions
diff --git a/buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m b/buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m new file mode 100644 index 0000000..e6e94db --- /dev/null +++ b/buch/chapters/40-eigenwerte/uebungsaufgaben/4003.m @@ -0,0 +1,66 @@ +# +# 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 = 2 +B = A - lambda*eye(4) +rref(B) + +D = B*B*B*B + +lambda = 3 +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 + |