Linear Algebra of Types

It gives my brain a pleasant thrum to learn new mathematics which mimics the algebra I learned in middle school. Basically this means that the new system has operations with properties that match those of regular numbers as much as possible. Two pretty important operations are addition and multiplication with the properties of distributivity and associativity. Roughly this corresponds to the mathe

[hamamuratakuo]

The reason i was even thinking about this is because we can lift the above construction to perform a linear algebra of vectors spaces. And I mean the spaces, not the vectors themselves. This is a confusing point.

[lotz84]

型レベル線形代数だと！？まぁオートマトンの状態遷移とかに使えそうなのかな🤔