https://gdpark.blog/tags/linear-maps/Recent content in Linear-Maps on gdpark.blogHugoenSun, 24 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-05-surjective-injective-and-bijective-functions/Wed, 20 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-05-surjective-injective-and-bijective-functions/We nail down surjective, injective, and bijective functions — and prove why same-dimension linear maps only need one condition to guarantee the other.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-08-change-of-basis/Fri, 22 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-08-change-of-basis/Same linear map, totally different matrix depending on your basis — let’s dig into why that happens and how A and A’ are actually related.https://gdpark.blog/posts/linear-algebra-09-systems-of-linear-equations-and-gaussian-elimination/Fri, 22 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-09-systems-of-linear-equations-and-gaussian-elimination/A casual walkthrough of systems of linear equations — from middle-school basics all the way up to matrix form, homogeneous vs. non-homogeneous, and Gaussian elimination.https://gdpark.blog/posts/linear-algebra-13-similar-matrices/Sun, 24 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-13-similar-matrices/Before we can actually crunch a determinant, we load up on similar matrices — plus why det A = 0 is the snap-decision test for invertibility.