Another text that starts with linear transformations is Apostol’s Calculus. It’s somewhat more concrete than Axler, IIRC — e.g. it doesn’t try to avoid determin

Another text that starts with linear transformations is Apostol’s Calculus. It’s somewhat more concrete than Axler, IIRC — e.g. it doesn’t try to avoid determinants, but starts with properties of volume-scaling and then develops the determinant formula out of those. We used this text for freshman/sophomore math back in the 80s, so my memory is fuzzy; but I liked it a lot.