Quantum Computing

Linear algebra that will be needed for the rest of thesis.\ud We begin by defining linear operators on vector spaces. we define physics Bra-Ket notation that\ud will be used throughout the thesis. The next few sections deal with topics related to matrices\ud like Trace,Unitary, Hermitian and Positive and Positive semi definite matrices. We define vector\ud spaces with some additional structures which includes inner product space, Outer product, Hilbert\ud space. we study how to make new spaces from the given spaces which includes direct sum of\ud vector spaces, Tensor product. Tensor product of spaces plays an important role in various area\ud of Quantum mechanics (we will study in next few chapters). we close this chapters with some\ud applications of Tensor product