For me, it helps to have some time before work where you can get stuff done. Of course you need to go to bed earlier, which is the tricky part. So shifting part of the free time to the morning hours.

why did they have to be weird about it and include odor?

I recently saw the THE as an abbreviation. Yes, THE. Terrible to read but made for funny sentences.

Key advantage of a diagonal matrix is that all off-diagonal entries are zero, so yes, no crossover of functions (or basis elements).

But the functions may be as ugly as they please and there may be an infinite number of them.

Sometimes, you can reorient your problem such that a matrix or tensor has only diagonal entries, making it easier to handle.

For example by choosing new unit vectors or by changing the set of functions describing the problem (whatever is the thing that the matrix or tensor is tied to).

You guys are allowed to say novel?!