The aim of this course is to introduce students to some special types of complex matrices such as normal matrices, Hermitian matrices, unitary matrices and to give them the ability to explain the algebraic differences and similarities between them. In addition, the aim of this course is to help students learn some special types of (linear) operators defined on inner product spaces and the basic properties of their adjoints.

Normal and Hermitian matrices, Unitary matrices, Unitary diagonalization of complex square matrices, Real symmetric matrices and orthogonal matrices, Real quadratic forms, Norm and its properties in inner product spaces, Orthogonal and orthonormal sets, Linear operators and their adjoints in inner product spaces, Normal operators, Hermitian operators, Unitary operators.