load lecture7 A A = 1 2 3 0 5 6 7 8 9 A'*A ans = 50 58 66 58 93 108 66 108 126 A*A ans = 22 36 42 42 73 84 70 126 150 A^2 ans = 22 36 42 42 73 84 70 126 150 A.*A ans = 1 4 9 0 25 36 49 64 81 A.^2 ans = 1 4 9 0 25 36 49 64 81 v=[3;4] v = 3 4 v'*v ans = 25 w=[1;2] w = 1 2 v v = 3 4 v'*w ans = 11 w'*v ans = 11 vLength=sqrt(v'*v) vLength = 5 v' ans = 3 4 v v = 3 4 errorVec=ASing*xSing errorVec = -4 24 20 errorVec=ASing*xSing-b errorVec = -7 22 11 abs(errorVec) ans = 7 22 11 max(abs(errorVec)) ans = 22 errorVec.^2 ans = 49 484 121 size(errorVec) ans = 3 1 errorVec errorVec = -7 22 11 prod(size(errorVec)) ans = 3 errorVec.^2 ans = 49 484 121 sum(errorVec.^2) ans = 654 sum(errorVec.^2)/prod(size(errorVec)) ans = 218 sqrt(sum(errorVec.^2)/prod(size(errorVec))) ans = 14.7648 max(abs(errorVec)) ans = 22 errorVec errorVec = -7 22 11 sqrt(errorVec'*errorVec)/prod(size(errorVec))) sqrt(errorVec'*errorVec)/prod(size(errorVec)))  {Error: Unbalanced or unexpected parenthesis or bracket. } sqrt(errorVec'*errorVec)/prod(size(errorVec)) ans = 8.5245 sqrt(errorVec'*errorVec/prod(size(errorVec))) ans = 14.7648 Big=[A A'] Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 BigSize=size(Big) BigSize = 3 6 Z=zeros(3,6) Z = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Z=zeros(BigSize) Z = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 Z+Big ans = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 zeros(3) ans = 0 0 0 0 0 0 0 0 0 [m n]=size(Big) m = 3 n = 6 Z=zeros(m) Z = 0 0 0 0 0 0 0 0 0 Z*Big ans = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 Z=zeros(n) Z = 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 0 0 0 Big*Z ans = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Z=zeros(m) Z = 0 0 0 0 0 0 0 0 0 Z=zeros(1,m) Z = 0 0 0 Z*Big ans = 0 0 0 0 0 0 Z=zeros(n,1) Z = 0 0 0 0 0 0 Big*Z ans = 0 0 0 eye(m) ans = 1 0 0 0 1 0 0 0 1 I=eye(m) I = 1 0 0 0 1 0 0 0 1 I*Big ans = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 I=eye(n) I = 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 Big*I ans = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 S = [3 4 5; 4 6 7' S = [3 4 5; 4 6 7; 5 7 8] S = 3 4 5 4 6 7 5 7 8 S' ans = 3 4 5 4 6 7 5 7 8 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 Big(2,3) ans = 6 big(2,2:4) {Undefined function or variable 'big'.} Big(2,2:4) ans = 5 6 2 Big(2,1:6) ans = 0 5 6 2 5 8 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 Big(2,1:6) ans = 0 5 6 2 5 8 Big(2,1:end) ans = 0 5 6 2 5 8 Big(2,:) ans = 0 5 6 2 5 8 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 Big(:,4) ans = 1 2 3 Big(:,[3 5]) ans = 3 0 6 5 9 6 Big(:,3:5) ans = 3 1 0 6 2 5 9 3 6 Big Big = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 BigDel(:,2:4)=[] {Deletion requires an existing variable.} BigDel=Big BigDel = 1 2 3 1 0 7 0 5 6 2 5 8 7 8 9 3 6 9 BigDel(:,2:4)=[] BigDel = 1 0 7 0 5 8 7 6 9 disp('Eigenvalues and Eigenvectors') Eigenvalues and Eigenvectors S = [0 1 0; 1 0 0; 0 0 0] S = 0 1 0 1 0 0 0 0 0 lambda=eig(S) lambda = -1 0 1 [E Lambda]=eig(S) E = -0.7071 0 0.7071 0.7071 0 0.7071 0 1.0000 0 Lambda = -1 0 0 0 0 0 0 0 1 evec1=E(:,1) evec1 = -0.7071 0.7071 0 evec2=E(:,2) evec2 = 0 0 1 evec3=E(:,3) evec3 = 0.7071 0.7071 0 lambda lambda = -1 0 1 Lambda Lambda = -1 0 0 0 0 0 0 0 1 lam1=lambda(1) lam1 = -1 lam2=lambda(2) lam2 = 0 lam3=lambda(3) lam3 = 1 lam1=Lambda(1,1) lam1 = -1 lam2=Lambda(2,2) lam2 = 0 Lambda Lambda = -1 0 0 0 0 0 0 0 1 lam3=Lambda(3,3) lam3 = 1 evec1 evec1 = -0.7071 0.7071 0 S*evec1 ans = 0.7071 -0.7071 0 lam2 lam2 = 0 evec2 evec2 = 0 0 1 S*evec2 ans = 0 0 0 lam3 lam3 = 1 evec3 evec3 = 0.7071 0.7071 0 S*evec3 ans = 0.7071 0.7071 0 S*evec3-evec3 ans = 0 0 0 max(abs(ans)) ans = 0 S S = 0 1 0 1 0 0 0 0 0 S' ans = 0 1 0 1 0 0 0 0 0 ltevec1=size(evec1) ltevec1 = 3 1 evec1 evec1 = -0.7071 0.7071 0 norm(evec1) ans = 1.0000 evac1.^2 {Undefined function or variable 'evac1'.} evec1.^2 ans = 0.5000 0.5000 0 sqrt(sum(evec1.^2)) ans = 1.0000 norm(evec1) ans = 1.0000 evec2 evec2 = 0 0 1 size(evec2) ans = 3 1 norm(evec1) ans = 1.0000 evec3 evec3 = 0.7071 0.7071 0 norm(evec3) ans = 1.0000 norm(evec2) ans = 1 evec1'*evec2 ans = 0 evec3'*evec2 ans = 0 [evec1 evec3] ans = -0.7071 0.7071 0.7071 0.7071 0 0 evec1'*evec3 ans = 0 S-S' ans = 0 0 0 0 0 0 0 0 0 S S = 0 1 0 1 0 0 0 0 0 A A = 1 2 3 0 5 6 7 8 9 eig(A) ans = 15.5440 -1.5440 1.0000 [E Lambda]=eig(A) E = -0.2401 -0.3201 0.3022 -0.4801 -0.6402 -0.7932 -0.8437 0.6983 0.5288 Lambda = 15.5440 0 0 0 -1.5440 0 0 0 1.0000 E(:1)'*E(:,2) E(:1)'*E(:,2)  {Error: Unexpected MATLAB expression. } E(:,1)'*E(:,2) ans = -0.2049