Exponential of Operators and Matrices

This lecture covers the exponential of operators and matrices, generalizing the exponential of a scalar to operators on inner product spaces. It explains the commutation properties of operators, the computation of exp(A) for diagonalizable matrices, and transforming defective matrices to Jordan normal form. The Jordan normal form is discussed, along with the computation of exp(A) using Jordan blocks. Linear algebra concepts related to linear operators, adjoint, eigenvalue problems, and the Spectral Theorem for normal operators are reviewed, emphasizing their importance in Quantum Mechanics and solving linear ODEs and PDEs.