00:01
All right, so recall that the annihilator, u to the zero, which is a subspace subset of v star, this is going to be the set of all linear functionals, f, which is an element of b star, such that f of u equal zero.
00:16
For all u in u and u to the zero plus w to the zero, that is the set f plus g, such that f is an element of the annihilator, u to the zero, and g is an element of w to the zero.
00:31
So for the proof here, we let fee be an element of u -inersect w -anilator.
00:45
So this means that fee of v is equal to zero for all v in the intersection, u -intersect, and then we want to extend fee to a sum f plus g where f is an element of u to the zero and g is an element of w to the zero so we can say that by the han an knock theorem in a finite dimension for subspaces u and v every linear functional vanishing on the intersection you intersect w can be written as a sum of one vanishing on u and one vanishing on w.
01:35
So we get that fee is an element of u to the 0 plus w to the zero, so we have then that u intersect w to the 0 is a subset of u to the 0 plus w to the 0...