and are parallel; paralelogram they span has area 0If , what can you say about ?
There's gotta be more?? Please tell me.
Are and meant as orthonormal vectors and ?If and , what's ?
If so, is this right: ??? Geometrically sounds right, in right-handed system , but I want to be sure.
If and what is ?
Please, check my scalar products:Are in-dependent? Do they make a basis in
So, they are in-dependent.
But, they don't make a basis because "there's not enough of them" () for 4D vector space; they don't span the whole space? OK, what's more rigorous answer?
In kernel is only , right?Let and be rotation of 90° around origin. Define kernel, image and rank of map .
Image is the whole ???
Rank of must be 2, otherwise it couldn't rotate (how could I better formalise my answer; if the 2 is correct of course)?
What should mean (what are and , obviously not points)?!
???Let be linear sub-space inside . Define orthogonal projection of to
???(Connects with previous quote.) Let also be ortho-normal basis for . Express projection (from previous) with this basis.