Thanks a lot with your two points I was able to proceed further.
https://github.com/Anand-GitH/HLL-QauntumComputing/blob/main/Qiskit-QPEStandalone.ipynb
I was able to find the eigen values of the two matrices with greater precision-
A=[[1,-1/3],[-1/3,1]]
Expected Eigen Values: [1.33333333 0.66666667]
Counts: {'11111111': 0.499999999999994, '11111110': 0.499999999999994}
Actual Eigen Value from Circuit:
1.3333333333333333
0.6614173228346456
A=[[1,-1/2],[-1/2,1]]
Expected Eigen Values: [1.5 0.5]
Counts: {'111': 0.500000000000001, '110': 0.500000000000001}
Actual Eigen Value from Circuit:
1.5
0.5
However, when I try other matrix: A = [[1.5, 0.5], [0.5, 1.5]]
Expected Eigen Values: [2. 1.]
Counts: {'011': 0.213388347648319, '010': 0.213388347648319}
Actual Eigen Value from Circuit:
2.0
0.6666666666666666
I do see there is so much difference in second eigen value.
If I use the same matrix in HHL to solve linear equation and match results with paper(https://www.sciencedirect.com/science/article/pii/S037596012030462X?via%3Dihub) it works absolutely fine.
https://github.com/Anand-GitH/HLL-QauntumComputing/blob/main/Qiskit-HHL.ipynb
I doubt now I am doing something wrong in reading out eigen values from QPE. Any suggestions on that part. I am just trying to read out all the eigen values of any matrix using qiskit EigsQPE.