https://gdpark.blog/tags/kernel/Recent content in Kernel on gdpark.blogHugoenSun, 31 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-06-kernel-and-image/Thu, 21 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-06-kernel-and-image/We nail down the kernel and image of a linear map, see what injective and surjective really mean, and lock in the theorem that links them all!!!!https://gdpark.blog/posts/linear-algebra-07-isomorphism-and-the-dimension-theorem/Thu, 21 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-07-isomorphism-and-the-dimension-theorem/Kernel and image lead us to isomorphism — two vector spaces with the same dimension and a bijective map between them are literally just the same space in disguise!!!!https://gdpark.blog/posts/linear-algebra-10-elementary-row-operation-matrices-erom/Sat, 23 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-10-elementary-row-operation-matrices-erom/Back at it with the general solution of AX = B — recapping RREF, breaking down dependent vs. independent variables, and chasing down X_0 and ker A.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.