Miracle of Linear Algebra

In this video, I present the two miracles of linear algebra: On the one hand, I show that every (finite-dimensional) vector space is isomorphic to R^n. In other words, every vector space, no matter how abstract, is just like a list of numbers. On the other hand, I show that every linear transformation is just like a matrix. So in some sense we’re bringing vectors and matrices back to life! This also explains why elementary linear algebra courses just focus on matrices! Enjoy!

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