The present disclosure describes methods and apparatuses for singular value decomposition with norm sorting. In some aspects, a sounding frame is received through a channel of a wireless medium. Based on the sounding frame, a channel covariance matrix describing conditions of the channel can be determined. The channel covariance matrix is then decomposed, with an ortho-normal matrix, to provide an intermediate matrix of vectors. One or more vectors of the intermediate matrix are sorted based on a respective norm to provide a norm-sorted matrix of the vectors. A steering matrix for the channel is then generated by ortho-normalizing at least two vectors of the norm-sorted matrix. By so doing, a steering matrix can be generated quickly and efficiently for use in subsequent communication operations.