This article proves an exponential probability tail inequality for positive semidefinite quadratic forms in a subgaussian random vector. The bound is analogous to one that holds when the vector has independent Gaussian entries.
"A tail inequality for quadratic forms of subgaussian random vectors." Electron. Commun. Probab. 17 1 - 6, 2012. https://doi.org/10.1214/ECP.v17-2079