At my (American, liberal arts, flyover country) university, linear algebra was my first real mathematics course.  (The prior classes were calculus and a &quot;proof&quot; class, AKA intro to intro to number theory.)  I&#x27;d been introduced to the determinant, Gauss--Jordan elimination, and so on, in high school, but all in a very mechanical way.<p>I think this transition between mechanically generating solutions to problems using pattern matching and some basic algorithms on the one hand, and the more mathematically mature approach of exploring problem spaces using pattern matching, some basic algorithms, and intuition can be difficult for many people.<p>It&#x27;s not necessarily the material -- you can get used to almost anything, and even convince yourself it&#x27;s easy or obvious with enough familiarity -- but the lack of intuition.  When you&#x27;re first learning linear algebra, its fundamental unity is not obvious, especially if the instructor does not take pains to point it out.  (And even if the instructor does take pains to point it out -- well, it&#x27;s hard to understand why the instructor is saying we could do this computation this way or that way.)  So in the absence of existing intuition or any perception of unity, linear algebra becomes another target for pattern matching and basic algorithms.<p>As it happens, I&#x27;ve never, ever felt like I didn&#x27;t &quot;get&quot; linear algebra.  However, I almost always feel like I &quot;get&quot; it now and all my prior conceptions of it were a confused muddle.