https://gdpark.blog/tags/vector-spaces/Recent content in Vector-Spaces on gdpark.blogHugoenThu, 21 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-01-vector-spaces/Mon, 18 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-01-vector-spaces/Turns out “linear” literally just means line-shaped — lol — and here’s why that embarrassingly simple idea is the backbone of basically all of math and STEM.https://gdpark.blog/posts/linear-algebra-02-linear-dependence-and-linear-independence/Tue, 19 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-02-linear-dependence-and-linear-independence/Breaking down linear combinations, span, and what it actually means for vectors to be linearly independent — all in plain terms.https://gdpark.blog/posts/linear-algebra-04-matrices-and-matrix-multiplication/Wed, 20 Jan 2016 00:00:00 +0000https://gdpark.blog/posts/linear-algebra-04-matrices-and-matrix-multiplication/We dive into linear algebra by unpacking functions as set mappings, then zoom in on linear mappings and how they all secretly boil down to matrices.https://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!!!!