answer 3 and 4

c. a=(22),b=(11), and c=(10),abc 3. The main difference between a Hilbert space and any random vector space is that a Hilbert space is equipped with an inner product, which is an operation that can be performed between two vectors, returning a scalar. For two vectors a and lb in a Hilbert space, we denote the inner a=a ). Thus, the inner product between two vectors of the Hilbert space looks something like: ab=(a1a2an)b1b2bn=a1b1+a2b2++anbn Calculate inner product of the following vectors in a Hilbert space. a) a=(20) and b=(02) b) a=(12) and b=(35) c) a=(1+i1) and b=(11+i) 4. The tensor product of vectors la) and b, written ab or ab, equals: ab=a1(b1b2)a2(b1b2)=a1b1a1b2a2b1a2b2 Calculate tensor product of the following two vectors: a) a=(20) and b=(02) b) a=(12) and b=(35) c) a=(1+i1) and b=(11+i)