Introduction to Quantum Mechanics · Problem A.10

Afterword — David J. Griffiths

Physics — Quantum Mechanics · matrices

Problem

By explicit construction of the matrices in question, show that any matrix

\mathsf{T}

can be written (a) as the sum of a symmetric matrix

\mathsf{S}

and an antisymmetric matrix

\mathsf{A}

; (b) as the sum of a real matrix

\mathsf{R}

and an imaginary matrix

\mathsf{M}

; (c) as the sum of a hermitian matrix

\mathsf{H}

and a skew-hermitian matrix

\mathsf{K}