This paper discusses the structure, calculation of multiplication and power, eigenvalue and eigenvector, and diagonalizable problems of matrix of rank equal to 1.
Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.
By using the result of the scalarization of the weak efficient solutions set, a result of the connectedness of the weak efficient solution sets is obtained in topological vector space.