PHY 404 Linear Spaces

Semester: Spring
Credit Hours: 2
Prerequisite: MTH 235 or equivalent

Vector, Banach, Hilbert spaces. Linear operators, Lebesque integral. Integral equations. Spectra.

syllabus

1. Vector spaces. Various definition of norm. Finite and infinite dimension. Banach spaces and Hilbert spaces. Spaces of linear operators.
2. Determinants. Permutations. Determinants and how to evaluate them. Subdeterminants of matrices. Inverse matrices.
3. Eigenvalues and Eigenvectors of matrices in N dimensions. Diagonalization. Unitary, Hermitian, symmetric, orthogonal matrices. Characteristic polynomials.
4. Operators in Hilbert spaces. Bounded operators, unitary operators. Diagonalization. Examples of bounded, selfadjoint, nondiagonalizable operators.
5. Bounded linear operators in Banach spaces. Functionals, dual spaces.
6. quantum mechanics and Hilbert spaces. Momentum and position operators. Continuous Eigenvalues of operators.

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