  This paper derives exponential concentration inequalities and polynomial
moment inequalities for the spectral norm of a random matrix. The analysis
requires a matrix extension of the scalar concentration theory developed by
Sourav Chatterjee using Stein's method of exchangeable pairs. When applied to a
sum of independent random matrices, this approach yields matrix generalizations
of the classical inequalities due to Hoeffding, Bernstein, Khintchine and
Rosenthal. The same technique delivers bounds for sums of dependent random
matrices and more general matrix-valued functions of dependent random
variables.
