Answer Happy

What do you mean by linearly independence of a set of vectors ? Consider three row vectors: (1, 1,0), (1, 0, 1) and (3,2,1). Are they linearly independent? Support your answer with details. Suppose u) and v) are two vectors in Hilbert space and (ulv) the inner product between these two vectors. Hence prove that the inner product is antilinear with respect to the first factor in the inner product. 2 Construct an orthogonal basis in two dimensions starting with Ẩ = 3î +4ĵ and B = î– 3ĵ. Can you generate orthonormal basis starting with these to vectors. Use Gram-Schmidt procedure to answer this question. Define Unitary operator. Prove that unitary operators preserve the inner product between the vectors they act on.