McCabe, Terence W.Chow, Chung Lim2024-05-072024-05-071993-05Chow, C.L. (1993). Symmetric linear transformations on Hilbert spaces (Unpublished thesis). Southwest Texas State University, San Marcos, Texas.https://hdl.handle.net/10877/18562The problem presented in this thesis is to characterize symmetric linear transformations on real Hilbert Space, i.e. a complete inner product space in which the scalar field is the real numbers. Additional conditions such as boundedness and compactness will be considered in our characterization. The following questions will be answered in this thesis: 1. What are the requirements for a symmetric bounded linear transformation to have eigenvalues? 2. Which symmetric linear transformation has a "square root"? Furthermore we will examine the kernel problem and the projection operator.Text52 pages1 file (.pdf)enHilbert spacedifferential equationsThesis