Modern Physics for Engineers Lecture slides 04c – Hermitian operators and sets of functions

This lecture part starts by introducing key ideas for working with complex matrices, especially the ideas of Hermitian adjoints and Hermitian matrices or, more generally, Hermitian operators. Such Hermitian operators are very useful for describing many physical systems, such as simple oscillators, and also later quantum mechanical systems. Among other properties, their eigenfunctions are orthogonal, and can represent, for example, the modes of many oscillating systems. Such eigenfunctions also generate mathematically complete and orthogonal basis sets for describing their corresponding physical systems - a very powerful property.