| ▲ | coderatlarge 6 hours ago | |
if you know how to handle real or complex coordinate vectors and matrices you’re one only isomorphism away (aka choice of basis) from dealing with an “abstract” vector space (except if you want to talk about finite fields or infinite dimensions). it seems like a really good starting point for many learners’ backgrounds… | ||
| ▲ | constantcrying 3 hours ago | parent | next [-] | |
>f you know how to handle real or complex coordinate vectors and matrices you’re one only isomorphism away (aka choice of basis) from dealing with an “abstract” vector space No, you aren't. How would you explain that matrices are both linear transformations and vectors? How would explain what a dual space is? How would you understand the properties of the Fourier transformation, which is a mapping between functions, which are also vectors, and itself also is a vector? | ||
| ▲ | coderatlarge 6 hours ago | parent | prev [-] | |
even Golub and van Loan basically start there. | ||