I/ Objectives:

Build a basic algorithm for finding an eigenvector and an eigenvalue of matrices within the framework of a diagonalization exercice.

II/ First version:

• With the value of c_1 found above define B = c_1 \* I - A where I is the identity matrix 2 by 2.
• Display the matrix B thus obtained.
• Repeat the same as in question 2 with this matrix B and new variables V_2, c_2 and W_2.
• display the final value of c_1 - c_2

III/ Second version:

• Assuming that A has two eigenvalues lambda_1 and lambda_2 with lambda_1 = c_1, what are the eigenvalues of B?
• Give approximate values of the eigenvalues of B.
• Deduce the second eigenvalue of A and an associated eigenvector.

IV/ Matrix calculus with Python:

Calculate the product Y = AX from the example given above and display the matrix A and the vectors X and Y.