The discussion revolves around proving the direct sum decomposition of a vector space, specifically showing that a vector space V can be expressed as the direct sum of two subspaces U and W derived from a basis B.
Some participants have provided guidance on the assumptions involved in the proof, while others are questioning the need to demonstrate certain assumptions, indicating a mix of understanding and confusion regarding the proof's requirements.
There is a focus on the definitions of the subspaces and the implications of their intersection, with some participants expressing uncertainty about the assumptions made in the problem statement.
You assume that v is nonzero - that's what "if v is nonzero" means. You don't need to show the things that you are assuming.ashina14 said:How can I show v is non zero?