Reddit reviews The Coordinate-Free Approach to Linear Models (Cambridge Series in Statistical and Probabilistic Mathematics)
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I don't have any books I would recommend on the m<n topic but if you want to deal with non-singular matrices, you need to pick up a book on the General Linear Model. I have been told Christiansen is good. I have also heard that Wichura is good but I don't think he does matrix theory very much. He is more interested in abstract vector spaces.