Introduction to Quantum Mechanics · Problem A.20

Afterword — David J. Griffiths

Physics — Quantum Mechanics · eigenvectors-eigenvalues

Problem

Show that the first, second, and last coefficients in the characteristic equation (Equation A.73) are:

C_n = (-1)^n, \quad C_{n-1} = (-1)^{n-1}\,\text{Tr}(\mathsf{T}), \quad \text{and} \quad C_0 = \det(\mathsf{T}).

For a

3 \times 3

matrix with elements

T_{ij}

, what is

C_1