▼ IMPORTANT ▼ How to diagonalize a matrix. I will first define what a diagonal matrix is, showing examples of 2x2, 3x3 and 4x4 square matrices. We will see a property that will allow us to quickly calculate powers of diagonalizable matrices. And we will see 4 simple steps to diagonalize a matrix, first by calculating the eigenvalues (eigenvalues, characteristic values, eigenvalues) solving the characteristic polynomial of the matrix, by developing a determinant, factoring and solving a general equation of the second degree. Then we calculate the eigenvectors (eigenvectors, eigenvectors, characteristic vectors) associated with these values, by solving a homogeneous system of linear equations with infinite solutions. Then we will form the matrices D and P, and finally we will calculate the inverse of P by means of a simple formula with a determinant (Adjoint formula). Once this is done, we will calculate the matrix raised to the exponent 5. Everything explained step by step.
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