What is here and how is defined for a matrix A?
In class we recently learned that for a linear operator and function one can define the operator (where is the identity transformation). We also recently learned about the exponential of a matrix. My question is that for a linear operator can the operator be defined? (For example, like how is defined for a matrix ) (I tried searching for information on it but all I found was information on the exponential of a matrix). Thanks.
Thanks.
Are you asking about operators on infinite-dimensional vector spaces? Because on a finite-dimensional space, every linear operator is given by a matrix, so the exponentiation of an operator is determined by the exponentiation of its matrix.