Multiple D$_p$-branes as a D$_{p+2}$-brane

From BFSS matrix theory considerations, it is expected that a single D$_{p+2}$-brane action can be obtained from N D$_p$-brane action in large N limit. We examine and confirm this expectation by working out the details of DBI and Chern-Simons terms of D$_{p+2}$-brane action from D$_{p}$-brane action. We show that the same relation works for non-BPS, as well as BPS branes