Website owner:  James Miller

                                 LINEAR OPERATORS

Existence of an inverse of a linear operator. The inverse A^-1 of a linear operator A exists if and only if Ax = 0 implies x = 0. In other words, the inverse exists if and only if the only element in the domain that is imaged into the element 0 is the element 0. When the inverse A^-1 exists it is a linear operator.

Null space of a linear operator. Let A be a linear operator whose domain is a vector space X and whose range is contained in a vector space Y. The null space of A is the set of all x in X such that Ax = 0 (i.e. it is the set of all vectors of the domain carried into zero by A). We denote this set by N(A).

Another term for “null space” is “kernel”.