Haha, you were so careful and still got the classic "That's not serious mathematics!" response. You might want something less applied, but I highly recommend B

Haha, you were so careful and still got the classic "That's not serious mathematics!" response. You might want something less applied, but I highly recommend Burden & Faires "Numerical Analysis" and Trefethen "Numerical Linear Algebra". The various interpretations provided by Trefethen for understanding a matrix, eigenvectors, singular value decompositions, etc. are amongst the most insightful descriptions I've come across.