Nonsquare matrices as transformations between dimensions | Essence of linear algebra, footnote
Because people asked, this is a video briefly showing the geometric interpretation of non-square matrices as linear transformations that go between dimensions.
==========
Hey, everyone! I've got another quick footnote for you between chapters today. When I talked about linear transformation so far, I've only really talked about transformations from 2-D vectors to other 2-D vectors, represented with 2-by-2 matrices; or from 3-D vectors to other 3-D vectors, represented with 3-by-3 matrices. But several commenters have asked about non-square matrices, so I thought I'd take a moment to just show with those means geometrically. By now in the series, you actually have most of the background you need to start pondering a question like this on your own. But I'll start talking through it, just to give a little mental momentum. It's perfectly reasonable to talk about transformations between dimensions, such as one that takes 2-D vectors to 3-D ...
==========
Hey, everyone! I've got another quick footnote for you between chapters today. When I talked about linear transformation so far, I've only really talked about transformations from 2-D vectors to other 2-D vectors, represented with 2-by-2 matrices; or from 3-D vectors to other 3-D vectors, represented with 3-by-3 matrices. But several commenters have asked about non-square matrices, so I thought I'd take a moment to just show with those means geometrically. By now in the series, you actually have most of the background you need to start pondering a question like this on your own. But I'll start talking through it, just to give a little mental momentum. It's perfectly reasonable to talk about transformations between dimensions, such as one that takes 2-D vectors to 3-D ...
