> My greatest wish in STEM education is that we teach linear algebra better.
That's easy. Vector spaces and linear transformations are best understood abstractly. Matrices are best understood as visually and computationally convenient representations of tensor products, so don't mention matrices at all until well after you have established the basic properties of tensor products, in particular, the natural isomorphism between `L(V,W)` and `Dual(V) (x) W`.
That's easy. Vector spaces and linear transformations are best understood abstractly. Matrices are best understood as visually and computationally convenient representations of tensor products, so don't mention matrices at all until well after you have established the basic properties of tensor products, in particular, the natural isomorphism between `L(V,W)` and `Dual(V) (x) W`.