-”On any finite dim space we have a canon inner product by taking the positive definite one.”
What? A finite dimensional space has more than one positive definite inner product (well, unless it is zero-dimensional), this choice is certainly not canonical. For example in R^2 any ellipse centered at the origin corresponds to a positive definite inner product.
On any finite dim space we have a canon inner product by taking the positive definite one.
Monad is a synonym for infinitesimal neighborhood, common on the literature. Not the category theory monad.
Also hermeneutic lmfao
-”On any finite dim space we have a canon inner product by taking the positive definite one.”
What? A finite dimensional space has more than one positive definite inner product (well, unless it is zero-dimensional), this choice is certainly not canonical. For example in R^2 any ellipse centered at the origin corresponds to a positive definite inner product.
I was thinking the one corresponding to a unit circle, just the ordinary dot product.
Canon is probably the wrong word in a mathy context.
Also yes the infinitesimal neighborhood of the identity.