I am a graduate student in math. I am coming up on the end of my masters, and multiple classes require LaTeX submissions. These classes are all very difficult by default, and spending multiple hours doing LaTeX only to submit an incomplete homework assignment feels non-constructive to me. I am ge...
> have found options like mathpix.com which will let me upload PDFs of my handwritten work, and then their AI will output LaTeX code which I can copy to overleaf and tweak for accuracy and formatting.
Someone commented (aptly :-)):
Could this be the most brilliant guerrilla marketing campaign ever? ;) — Ianyesterday
When I first learnt linear models, I confess I didn't like it due to those intimidating formulae, the derivations of which were equally intimidating even though the concepts needed were pre-algebra routine calculations.
But then I got a whole new sleek outlook of all these when working with orthogonal projection operators. They are far more intuitive, rigorous and yets maintains the appeal from geometric pov.
Early undergrad books had a dearth of such treatments. But today authors like Ronald Christensen do a fabulous job in developing the whole theory of linear models from that perspective. One can check his book:
More appealing (than Lagrangian multipliers), intuitive from a geometrical point of view is to resort to perpendicular projection operators.
It is apt to work in a more general setting: let us consider for the linear model $$\mathbf Y = \mathbf X\boldsymbol\beta +\boldsymbol{\varepsilon},$$ the h...
Although, to be fair, these are not some new techniques. They were already present over the century. Just that they were under represented in (at least) introductory books.
