Linear precoding is a relatively simple method of MIMO signaling that can also be optimal in certain special cases. This paper is dedicated to high-SNR analysis of MIMO linear precoding. The Diversity-Multiplexing Tradeoff (DMT) of a number of linear precoders is analyzed. Furthermore, since the diversity at finite rate (also known as the fixed-rate regime, corresponding to multiplexing gain of zero) does not always follow from the DMT, linear precoders are also analyzed for their diversity at fixed rates. In several cases, the diversity at multiplexing gain of zero is found not to be unique, but rather to depend on spectral efficiency. The analysis includes the zero-forcing (ZF), regularized ZF, matched filtering and Wiener filtering precoders. We calculate the DMT of ZF precoding under two common design approaches, namely maximizing the throughput and minimizing the transmit power. It is shown that regularized ZF (RZF) or Matched filter (MF) suffer from error floors for all positive multiplexing gains. However, in the fixed rate regime, RZF and MF precoding achieve full diversity up to a certain spectral efficiency and zero diversity at rates above it. When the regularization parameter in the RZF is optimized in the MMSE sense, the structure is known as the Wiener precoder which in the fixed-rate regime is shown to have diversity that depends not only on the number of antennas, but also on the spectral efficiency. The diversity in the presence of both precoding and equalization is also analyzed.