Talk:Dual list

Null-space?

I'm confused. This article seems to be giving an elaborate alternative to the null-space of a matrix. Am I misunderstanding? What use or additional insight does this method provide beyond taking the null-space? (when going from the comma basis back to the mapping, it's necessary to sandwich the null-space operation with anti-transposes)

The first example seems clearly wrong, because dimensionality is 5 (each map and comma has 5 elements) yet the temperament is rank-3 (there are 3 maps) and has nullity 3 (there are three commas). The rank and nullity must sum to the dimensionality. --Cmloegcmluin (talk) 01:25, 16 June 2021 (UTC)

I'm pretty sure the conversion from the val list to the monzo list is simply taking the null space. I haven't studied how to convert backwards, and I abs wonder.

The first example contains a redundant row in the val list. That 72 is simply 31 + 41. FloraC (talk) 06:26, 16 June 2021 (UTC)

Thanks, FloraC. Good catch on the redundant mapping row. Maybe it was intentional, to show how the process returns the appropriate null-space anyway. I suppose that's valuable to demonstrate. I'm just surprised it's the first example, then, and not mentioned. I'll just add an explanatory note. --Cmloegcmluin (talk) 15:40, 16 June 2021 (UTC)