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1. ### Can a subcategory be an ideal?

Consider a category C with objects ob(C) and morphisms hom(C). Suppose there is a subcategory D such that ob(D)=ob(C) but hom(D) is a subset of hom(C), with the property that the product of two morphisms in hom(C), f*g, is an element of hom(D) if either f or g is in hom(D). This subcategory is...
2. ### Projection onto the kernel of a matrix

Dear Fredrik, Thank you for the reply. I think I was not sufficiently clear about the concept I am considering. I want to consider a linear operator M on a vector space V whose image is linearly independent from its Kernel. On a finite dimensional vector space, this implies that V = ker M +...
3. ### Projection onto the kernel of a matrix

If we have a matrix M with a kernel, in many cases there exists a projection operator P onto the kernel of M satisfying [P,M]=0. It seems to me that this projector does not in general need to be an orthogonal projector, but it is probably unique if it exists. My question: is there a standard...