In a multicore system, will each cpu have its own linux kernel?

"Thank you all for your answers. I did a little research myself and found that both are possible in multicore systems. A SMP multicore system will have a single linux kernel for all the cores, where as in an AMP multicore system, each core will have its own kernel. Typically,some multicores will have couple of cores for AMP performing real time critical tasks, and the rest will be SMP performing non critical and normal tasks.

The question, i asked is about kernel tracing. Nowadays, most kernels come with inbuilt kprobes that will allow kernel developers to get information about the kernel performance. I guess, the answer to the first question also solves this question. In a SMP, a single trace for a kernel will be generated where as in AMP, as many traces as the number of cpu's will be generated.

AMP stands for Asymmetric Multi Processing, SMP stands for Symmetric Multi Processing"