Numerical Linear Algebra seems to be a very active area right now, but is there any work still being done on the purely theoretical side?
To put it another way...is it possible for someone to write a book titled "All of Linear Algebra" and actually create a closed set of concepts that encompass this field?
For example, I'm thinking a book like Peter Lax's Linear Algebra and its Applications seems to be close to this, but a lot of reviewers of the book stated it was a select group of topics.
I searched MathSciNet. Classification 15 is "Linear and multilinear algebra; matrix theory". There are (so far) more than 400 papers dated 2015 with that classification.
a few examples
Hora, Jan; Pudlák, Petr; Classification of 8-dimensional Trilinear Alternating Forms over GF(2). Comm. Algebra 43 (2015), no. 8, 3459–3471.
Farber, Miriam; Berman, Abraham; A contribution to the connections between Fibonacci numbers and matrix theory. Involve 8 (2015), no. 3, 491–501.
Bu, Changjiang; Wei, Yuanpeng; Sun, Lizhu; Zhou, Jiang; Brualdi-type eigenvalue inclusion sets of tensors. Linear Algebra Appl. 480 (2015), 168–175.