How to think about indices and cartesian coordinates?

It is really neither correct nor incorrect, it is really up to you to choose a convention for yourself. Unfortunately.

The problem is that we are used to thinking of x as the first dimension and y as the second dimension, while in linear algebra the first dimension is ‘downwards’ and the second dimension is ‘across’.

Every time, I struggle with choosing a convention, and I personally believe everything would be much nicer if the first index always was the x-direction, and also indicated column (the opposite of today).

So, it’s up to you.

I urge you to not get into the habit of using collect. It is wasteful and pointless here. Forget you ever heard of that function. Remove it from all your codes, and don’t use until your code stops working without it.

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