At the beginning of this video, the instructor gives an interesting explanation of Left Nullspace...
"What Left Nullspace is...these are the known unknowns of Left Nullspace; the unbuildable reality. Alright, this is the stuff that, if you're thinking, and you see things out in the world, these are the things that ???? past you, because you don't have building blocks, right? These are the building blocks we're missing. We can't capture them. These are the sounds you can't hear...Of course it's all linear, but it's nice to think about it more generally."
I understand that Column Space is the set of all vectors that can be output by a given linear transformation, and that Nullspace is the set of all input vectors it can transform into the zero vector, and of course, one visual intuition of Row Space and Left Nullspace would be a composition of each of these transformations with a transpose, but this quote seems to be describing a more direct picture of the latter. How can this quote be expanded to give a more direct understanding of the role of Left Nullspace in a linear transformation?
"What Left Nullspace is...these are the known unknowns of Left Nullspace; the unbuildable reality. Alright, this is the stuff that, if you're thinking, and you see things out in the world, these are the things that ???? past you, because you don't have building blocks, right? These are the building blocks we're missing. We can't capture them. These are the sounds you can't hear...Of course it's all linear, but it's nice to think about it more generally."
I understand that Column Space is the set of all vectors that can be output by a given linear transformation, and that Nullspace is the set of all input vectors it can transform into the zero vector, and of course, one visual intuition of Row Space and Left Nullspace would be a composition of each of these transformations with a transpose, but this quote seems to be describing a more direct picture of the latter. How can this quote be expanded to give a more direct understanding of the role of Left Nullspace in a linear transformation?
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