Homework Help Overview
The discussion revolves around a linear map A from vector space V to vector space W, with given dimensions for both spaces. The original poster seeks to determine the dimension of the kernel of the linear map under the condition that A is onto.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the implications of the map being onto and consider the relationship between the dimensions of the kernel and image. There is an attempt to apply the rank-nullity theorem to derive the dimension of the kernel.
Discussion Status
Some participants have offered insights regarding the rank-nullity theorem, while others are exploring the potential dimension of the kernel based on the dimensions of V and W. Multiple interpretations of the kernel's dimension are being discussed without reaching a consensus.
Contextual Notes
There is an assumption that the dimensions of the vector spaces V and W are known, but the specific values are not provided. The discussion also reflects on the implications of the linear map being onto.