Strang’s textbook (and lectures) introduce matrix multiplication AB as combinations of A’s columns. He uses the cell-by-cell / “dot product” formulas just to check his work, which seems reasonable to me. I’m a big fan of “combinations of columns”. I sometimes even hear that in Strang’s voice when I’m doing some matrix multiplications.
Axler was way too abstract for me as a first linear algebra book. I look forward to returning to it once I finish Strang.
Strang's exposition can make you a wizard of matrix multiplication and give you quite a good intuition for various properties of matrix operations, in my opinion.
Axler was way too abstract for me as a first linear algebra book. I look forward to returning to it once I finish Strang.