Similar Matrices & Matrix Powers

Linear Algebra for Machine Learning · Axiom Academy

Diagonalizing a Specific Matrix Diagonalize the following matrix (find P and D such that A = PDP⁻¹): The diagonalization A = PDP⁻¹ reveals the "natural" basis of the matrix. In this basis (the eigenvector basis), the matrix is diagonal, which means: The transformation only stretches along the eigenvector directions There's no mixing between different eigenvector directions Computing powers is trivial: A¹⁰ = PD¹⁰P⁻¹

This is the written version of the interactive lesson above. See the full Linear Algebra for Machine Learning course.