https://gdpark.blog/tags/diagonalization/Recent content in Diagonalization on gdpark.blogHugoenSun, 31 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-16-block-matrices/Wed, 27 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-16-block-matrices/A casual dive into diagonalization — what it means to turn a matrix diagonal, why that’s such a big deal in physics, and how blocking gets the whole thing started.https://gdpark.blog/posts/linear-algebra-17-introduction-to-diagonalization-eigenvalues-and-eigenvectors/Thu, 28 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-17-introduction-to-diagonalization-eigenvalues-and-eigenvectors/Finally cracking how to diagonalize a matrix without hunting for the right basis — turns out eigenvalues and eigenvectors are the secret the whole time!https://gdpark.blog/posts/linear-algebra-18-characteristic-polynomials-and-the-cayley-hamilton-theorem/Fri, 29 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-18-characteristic-polynomials-and-the-cayley-hamilton-theorem/We chase down which matrices can actually be diagonalized — starting with characteristic polynomials, hitting complex eigenvalues, and landing on the Cayley–Hamilton theorem.https://gdpark.blog/posts/linear-algebra-20-the-first-decomposition-theorem/Sun, 31 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-20-the-first-decomposition-theorem/We revisit diagonalization up close — eigenvalues, kernels, and how a 2D space splits into two 1D invariant subspaces — as a warm-up for the full Decomposition Theorem.