Vectors, what even are they? | Essence of linear algebra, chapter 1
I imagine many viewers are already familiar with vectors in some context, so this video is intended both as a quick review of vector terminology, as well as a ...
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"The introduction of numbers as coordinates is an act of violence." —Hermann Weyl The fundamental, root-of-it-all building block for linear algebra is the vector, so it's worth making sure that we're all on the same page about what exactly a vector is. You see, broadly speaking there are three distinct but related ideas about vectors, which I'll call the physics student perspective, the computer science student perspective, and the mathematician's perspective. The physics student perspective is that vectors are arrows pointing in space. What defines a given vector is its length, and the direction it's pointing in, but as long as those two facts are the same, you can move it all around and it's still the same vector. Vectors that live in the flat p...
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"The introduction of numbers as coordinates is an act of violence." —Hermann Weyl The fundamental, root-of-it-all building block for linear algebra is the vector, so it's worth making sure that we're all on the same page about what exactly a vector is. You see, broadly speaking there are three distinct but related ideas about vectors, which I'll call the physics student perspective, the computer science student perspective, and the mathematician's perspective. The physics student perspective is that vectors are arrows pointing in space. What defines a given vector is its length, and the direction it's pointing in, but as long as those two facts are the same, you can move it all around and it's still the same vector. Vectors that live in the flat p...
