Function Spaces and Matrices

ThisFunction space chapter refreshes such necessary algebraic knowledge as will be needed in this book. It introduces function spacesFunction space and their adjoints, the meaning of a linear operatorOperatorlinear, and the properties of unitary matricesMatrixunitary. The homomorphismHomomorphism between operations and matrix multiplications is established, and the DiracDirac notation for function spacesFunction space is defined. For those who might think that the linearity of operators is obvious, the final section introducesTime reversal time reversalReversaltime, which is anti-linear.