Just this year I read that a new insight about eigenvalues/eigenvectors had just been discovered, shocking the math world that a new insight from linear algebra could be discovered.
Here is a write-up by Terry Tao. This doesn't disprove the premise that linear algebra is more or less solved. Although the result was unknown and a little surprising, once formulated the proof was relatively straightforward, and does not imply any major or minor upsets in the field.
