41. In particular it states that requiring a bounded linear operator on a complex Hilbert space to satisfy 42. In mathematical jargon, the derivative is a linear operator which inputs a function and outputs a second function. 43. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. 44. An important object of study in functional analysis are the linear operators defined on Banach and Hilbert spaces. 45. Consider a continuous linear operator ( for linear operators , continuity is equivalent to being a bounded operator ). 46. Mathematically, tensors are generalised linear operators -maps. 47. Define a linear operator as follows: 48. Consider a continuous linear operator ( for linear operators, continuity is equivalent to being a bounded operator ). 49. This product appears frequently in linear algebra and applications, such as matrix representations of the same linear operator . 50. Let \ mathcal { L } denote the class of continuous linear operators acting between two Banach spaces.
