I found that the level of abstraction that linear algebra is taught at is really weird.  On the one hand it was never really taught in connection with algebra in general, or put into a wider mathematical context.  On the other hand we were never really shown any real world used of linear algebra or how the concepts maps onto practical applications.<p>It wasn&#x27;t before years later when A) I&#x27;d taken more abstract algebra courses that introduced concepts like tensors and fields and B) I&#x27;d taken more practical computational courses where I had to do things like use linear algebra in 3D graphics and use eigenvectors to do dimensionality reduction and PCA, that I really understood the subject and its place in the world.<p>Just saying here&#x27;s a random object (that we&#x27;ll call a &quot;matrix&quot;), here&#x27;s some random steps (that we&#x27;ll call &quot;taking a determinant&quot;), now memorize how to apply the steps to the object and see if the result is zero, didn&#x27;t lead to much deeper understanding.