TestComplexMatrix.java running
Matrix A
A[0][0]=(0.0,0.0)
A[0][1]=(1.0,2.0)
A[0][2]=(2.0,4.0)
A[0][3]=(3.0,6.0)
A[1][0]=(2.0,1.0)
A[1][1]=(2.0,2.0)
A[1][2]=(3.0,4.0)
A[1][3]=(4.0,6.0)
A[2][0]=(4.0,2.0)
A[2][1]=(4.0,3.0)
A[2][2]=(4.0,4.0)
A[2][3]=(5.0,6.0)
A[3][0]=(6.0,3.0)
A[3][1]=(6.0,4.0)
A[3][2]=(6.0,5.0)
A[3][3]=(6.0,6.0)
inverse of A
A[0][0]=(-0.4666666666666667,0.4666666666666667)
A[0][1]=(0.4999999999999998,-0.5000000000000002)
A[0][2]=(4.625929269271487E-16,4.625929269271483E-16)
A[0][3]=(-0.033333333333333555,0.09999999999999969)
A[1][0]=(0.4999999999999998,-0.4999999999999997)
A[1][1]=(-0.9999999999999993,1.0000000000000002)
A[1][2]=(0.49999999999999906,-0.5000000000000009)
A[1][3]=(3.608224830031759E-16,6.38378239159465E-16)
A[2][0]=(4.996003610813202E-16,-4.996003610813206E-16)
A[2][1]=(0.49999999999999906,-0.4999999999999995)
A[2][2]=(-0.9999999999999996,1.0000000000000004)
A[2][3]=(0.5,-0.5000000000000004)
A[3][0]=(-0.1000000000000002,0.03333333333333355)
A[3][1]=(3.0531133177191805E-16,-3.608224830031759E-16)
A[3][2]=(0.5,-0.5)
A[3][3]=(-0.3333333333333334,0.3333333333333334)
check A * A^-1 = I
A[0][0]=(1.0000000000000004,2.220446049250313E-16)
A[0][1]=(-9.159339953157541E-16,-4.718447854656915E-16)
A[0][2]=(0.0,0.0)
A[0][3]=(0.0,2.220446049250313E-16)
A[1][0]=(6.661338147750939E-16,2.7755575615628914E-16)
A[1][1]=(0.9999999999999993,-7.216449660063518E-16)
A[1][2]=(0.0,7.771561172376096E-16)
A[1][3]=(4.440892098500626E-16,-2.220446049250313E-16)
A[2][0]=(1.1102230246251565E-16,3.3306690738754696E-16)
A[2][1]=(-7.494005416219807E-16,-4.163336342344337E-16)
A[2][2]=(1.0,-1.1102230246251565E-16)
A[2][3]=(0.0,2.220446049250313E-16)
A[3][0]=(1.1102230246251565E-15,3.885780586188048E-16)
A[3][1]=(-2.220446049250313E-15,3.3306690738754696E-16)
A[3][2]=(0.0,-4.440892098500626E-16)
A[3][3]=(1.0,0.0)

initial matrix A
A[0][0]=(1.0,1.0)
A[0][1]=(2.0,1.0)
A[0][2]=(3.0,1.0)
A[0][3]=(4.0,1.0)
A[1][0]=(2.0,1.0)
A[1][1]=(2.0,2.0)
A[1][2]=(3.0,2.0)
A[1][3]=(4.0,2.0)
A[2][0]=(3.0,1.0)
A[2][1]=(3.0,2.0)
A[2][2]=(3.0,3.0)
A[2][3]=(4.0,3.0)
A[3][0]=(4.0,1.0)
A[3][1]=(4.0,2.0)
A[3][2]=(4.0,3.0)
A[3][3]=(4.0,4.0)
initial vector Y
X[0]=(30.0,0.0)
X[1]=(31.0,0.0)
X[2]=(34.0,0.0)
X[3]=(40.0,0.0)
solve equations Y = A X
X = solution
X[0]=(1.4999999999999991,-6.500000000000001)
X[1]=(1.0000000000000027,1.0000000000000009)
X[2]=(1.4999999999999982,1.5)
X[3]=(4.000000000000001,-2.0000000000000004)
check that solution gives back Y
X[0]=(30.0,0.0)
X[1]=(31.0,0.0)
X[2]=(34.00000000000001,0.0)
X[3]=(40.00000000000001,3.552713678800501E-15)
check for zero A*X-Y vector
X[0]=(0.0,0.0)
X[1]=(0.0,0.0)
X[2]=(7.105427357601002E-15,0.0)
X[3]=(7.105427357601002E-15,3.552713678800501E-15)
invert(A)
A[0][0]=(-0.6,-0.6)
A[0][1]=(0.5,0.5)
A[0][2]=(-5.551115123125783E-17,-5.551115123125783E-17)
A[0][3]=(0.1,-0.1)
A[1][0]=(0.5,0.5)
A[1][1]=(-1.0,-1.0)
A[1][2]=(0.5,0.5)
A[1][3]=(0.0,-0.0)
A[2][0]=(-5.551115123125783E-17,-5.551115123125783E-17)
A[2][1]=(0.5,0.5)
A[2][2]=(-0.9999999999999999,-0.9999999999999999)
A[2][3]=(0.5,0.5)
A[3][0]=(0.1,-0.1)
A[3][1]=(-0.0,0.0)
A[3][2]=(0.5,0.5)
A[3][3]=(-0.4,-0.4)
check for solution vector, using invert(A) * Y
X[0]=(1.4999999999999982,-6.500000000000002)
X[1]=(1.0,1.0)
X[2]=(1.500000000000007,1.500000000000007)
X[3]=(4.0,-2.0)
check for zero A^-1*Y-X vector
X[0]=(-8.881784197001252E-16,-8.881784197001252E-16)
X[1]=(-2.6645352591003757E-15,-8.881784197001252E-16)
X[2]=(8.881784197001252E-15,7.105427357601002E-15)
X[3]=(-8.881784197001252E-16,4.440892098500626E-16)
invert(AI) should be A
A[0][0]=(1.0,1.0)
A[0][1]=(2.0,1.0)
A[0][2]=(3.0,1.0)
A[0][3]=(4.0,1.0)
A[1][0]=(2.0,1.0)
A[1][1]=(2.0,2.0)
A[1][2]=(3.0,2.0)
A[1][3]=(4.0,2.0)
A[2][0]=(3.0,1.0)
A[2][1]=(3.0,2.0)
A[2][2]=(3.0,3.0)
A[2][3]=(4.0,3.0)
A[3][0]=(4.0,1.0)
A[3][1]=(4.0,2.0)
A[3][2]=(4.0,3.0)
A[3][3]=(4.0,4.0)
check for zero ((A^-1)^-1)-A check
A[0][0]=(0.0,0.0)
A[0][1]=(0.0,0.0)
A[0][2]=(0.0,0.0)
A[0][3]=(0.0,0.0)
A[1][0]=(0.0,0.0)
A[1][1]=(0.0,0.0)
A[1][2]=(0.0,0.0)
A[1][3]=(0.0,0.0)
A[2][0]=(0.0,0.0)
A[2][1]=(0.0,0.0)
A[2][2]=(0.0,0.0)
A[2][3]=(0.0,0.0)
A[3][0]=(0.0,0.0)
A[3][1]=(0.0,0.0)
A[3][2]=(0.0,0.0)
A[3][3]=(0.0,0.0)
norm of ((A^-1)^-1)-A 0.0

initial matrix A2
A[0][0]=(1.0,0.0)
A[0][1]=(2.0,0.0)
A[0][2]=(3.0,0.0)
A[1][0]=(4.0,0.0)
A[1][1]=(5.0,0.0)
A[1][2]=(6.0,0.0)
A[2][0]=(4.0,0.0)
A[2][1]=(4.0,0.0)
A[2][2]=(4.0,0.0)
initial vector Y2
X[0]=(1.5,0.0)
X[1]=(2.5,0.0)
X[2]=(3.5,0.0)
solving equations
redundant row (singular) 0
X2 = solution of Y2=A2 X2
X[0]=(1.875,0.0)
X[1]=(-1.0,-0.0)
X[2]=(0.0,0.0)
check that solution gives back Y2
X[0]=(-0.125,0.0)
X[1]=(2.5,0.0)
X[2]=(3.5,0.0)
check for zero vector
X[0]=(-1.625,0.0)
X[1]=(0.0,0.0)
X[2]=(0.0,0.0)
ComplexMatrix is singular !
expect singular matrix 


D = determinant(A)
D= (-8.881784197001252E-16,10.0)
D=determinant(A2)
D= (-0.0,0.0)

eigenvalues
check for near zero norm of Z[0]=3.1051550219984847E-16
check for near zero norm of Z[1]=-2.498001805406602E-16
check for near zero norm of Z[2]=4.440892098500626E-16
check for near zero norm of Z[3]=2.8421709430404007E-14
eigenvalues from polynomial
check for |A||v|-y[i]|v| near zero i=0, norm= 1.0
check for |A||v|-y[i]|v| near zero i=1, norm= 38.48376280978771
check for |A||v|-y[i]|v| near zero i=2, norm= 22.02271554554524
check for |A||v|-y[i]|v| near zero i=3, norm= 7.0710678118654755
norm =68.57754616719842 is eigen vector total error indication
det V = (1.0,0.0)
check for vector length 1.0 = 1.0
check for vector length 1.0 = 1.0
check for vector length 1.0 = 1.0
check for vector length 1.0 = 1.0
norm =60764.23717944627 is eigen value total error indication.
norm1=6.42
norm2=5.299566019968051
normInf=5.15

norm1=16.0
norm2=9.486832980505138
normInf=17.0
normFro=15.0

identity matrix
A[0][0]=(1.0,0.0)
A[0][1]=(0.0,0.0)
A[0][2]=(0.0,0.0)
A[1][0]=(0.0,0.0)
A[1][1]=(1.0,0.0)
A[1][2]=(0.0,0.0)
A[2][0]=(0.0,0.0)
A[2][1]=(0.0,0.0)
A[2][2]=(1.0,0.0)
zero matrix
A[0][0]=(0.0,0.0)
A[0][1]=(0.0,0.0)
A[0][2]=(0.0,0.0)
A[1][0]=(0.0,0.0)
A[1][1]=(0.0,0.0)
A[1][2]=(0.0,0.0)
A[2][0]=(0.0,0.0)
A[2][1]=(0.0,0.0)
A[2][2]=(0.0,0.0)
unit vector [1]
X[0]=(0.0,0.0)
X[1]=(1.0,0.0)
X[2]=(0.0,0.0)
zero vector
X[0]=(0.0,0.0)
X[1]=(0.0,0.0)
X[2]=(0.0,0.0)
TestComplexMatrix finished