00:01
Let's prove that the only element, w in an inner product space v, that is orthogonal to every vector, that is w times v, times means here, inner product, equals zero for all v in vector space v is a zero vector.
00:20
That is, w got to be equal to zero.
00:24
If this is true for every vector in the vector space.
00:30
So that comes, in fact, from the properties of the inner product.
00:35
So if this argument this way, if the inner product of w times v is zero for all vectors in v, then w is a vector in v.
00:52
So this got to be true for w.
00:56
As w is in b, you must have that the inner product of w times itself.
01:08
Is zero because that property is true for any vector v in the vector space v, in particular for w, which is a vector in v...
