The discussion revolves around linear transformations and their properties, specifically focusing on the kernel of a transformation and the implications of injectivity and surjectivity on invertibility.
Participants are exploring the definitions and implications of linear transformations, with some providing clarifications on the dimension of the kernel and the conditions under which a transformation can be considered invertible. Multiple interpretations regarding injectivity and surjectivity are being discussed.
There is a focus on technical definitions and properties of linear transformations, with an emphasis on the implications of these properties in different dimensional contexts.
Just one more thing, if a transformation is injective then it is not necessarily onto?
I ask this because I would like to know if in determining whether a transformation is invertible, if it is sufficient to look at whether or not it is injective.