Vectors are the fundamentals in a Hilbert space. They represent the state of a physical system corresponding to that Hilbert space. But a state or a vector is passive. What is interesting is the application of an operator to rotate the vectors in the space or, in other words, to transform the state. An operator corresponds to a matrix. In this chapter, we will review the concepts of eigenvalue, eigenvector, Hermitian matrix, and unitary matrix. We will also review how to construct a projection operator and a unitary transformation matrix. Then we will revisit the meaning of a measurement in a quantum system using the new knowledge we have learned. Finally, we will discuss how to perform a tensor product for matrices.