QR Algorithm for Eigenvalues and Eigenvectors

Project Title:
Development of a QR Algorithm for Eigenvalues and Eigenvectors in Python (No Built-In NumPy Functions)

Project Description:
I'm seeking a Python expert to develop a QR algorithm for finding eigenvalues and eigenvectors of a symmetric matrix. The input will be an n × n matrix
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M and a precision parameter
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ϵ. The output should be:

A matrix
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V containing the eigenvectors.
A vector containing the eigenvalues of
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M.
Key Requirements:

Proficient in Python.
Do not use NumPy's built-in functions for matrix operations related to QR decomposition, eigenvalue, or eigenvector computation.
Experience in implementing numerical algorithms from scratch.
Skilled in optimizing algorithms for performance (focus on efficiency over readability).
The final solution should allow for adjustable precision
�
ϵ.
Deliverables:

Python code implementing the QR algorithm, ensuring accurate and efficient computation of eigenvalues and eigenvectors.
Documentation explaining the approach, especially focusing on the implementation of matrix operations without relying on NumPy's built-in functions.