Decomposition of spectrum functional analysis

In functional analysis, the spectrum of a linear operator is a fundamental concept of linear algebra. The spectrum consists of all scalars. Decomposition is relevant to the study of differential equations, and has applications to many branches of science and engineering. This is an explanation of discrete spectral lines and the continuous band in the light emitted by excited atoms of hydrogen. The definition of linear operators is based on a concept from functional analysis. The word spectrum is the spectrum that allows us to study operators on a Banach space. The notation T is the operator's spectrum, or spectrum, of a Banac operator in the space of operators. The term linear operator was introduced by Charles Guthry in his seminal work "The Structure of the Cartesian Plane" in 1947.