Going from Strang to D&F seems like a steep jump. The former is an applied textbook for non-mathematicians and the latter is a proof-based text for advanced undergraduate / graduate-level math students.
I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.
I would suggest working through a proof-based linear algebra book in between to ease the transition. Axler's is a good one. Alternatives include Hoffman and Kunze and the more modern Friedberg, Insel, and Spence.