A function f is called a linear operator if it has the two properties: f(x+y)=f(x)+f(y) for all x and y; f(cx)=cf(x) for all x and all constants c.
What is linear operator with examples?
Examples: The simplest linear operator is the identity operator I. I|V> = |V>, <V|I = <V|. The parity operator ∏, operating on elements ψ(x,y,z) of L2, is a linear operator.
What is linear operator equation?
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. ... The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis.
