https://gdpark.blog/tags/characteristic-polynomial/Recent content in Characteristic-Polynomial on gdpark.blogHugoenTue, 02 Feb 2016 00:00:00 +0000https://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.https://gdpark.blog/posts/linear-algebra-21-minimal-polynomials-companion-matrices-and-more/Mon, 01 Feb 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-21-minimal-polynomials-companion-matrices-and-more/Diving into minimal polynomials and their sneaky relationship with characteristic polynomials — turns out it’s the same divisor-hunting logic we used back in number theory!!!!https://gdpark.blog/posts/linear-algebra-22-is-further-block-decomposition-always-possible/Tue, 02 Feb 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-22-is-further-block-decomposition-always-possible/Poking at a special case where the minimal and characteristic polynomials match as a power of an irreducible polynomial, and what that tells us about block decomposition.