  We compute the minimal log discrepancies of determinantal varieties of square
matrices, and more generally of pairs $\bigl(D^k,\sum \alpha_i D^{k_i}\bigr)$
consisting of a determinantal variety (of square matrices) and an $\mathbb
R$-linear sum of determinantal subvarieties. Our result implies the
semicontinuity conjecture for minimal log discrepancies of such pairs. For
these computations, we use the description of minimal log discrepancies via
codimensions of cylinders in the space of jets; this necessitates the
computations of an explicit generator for the canonical differential forms and
the Nash ideal of determinantal varieties, which may be of independent
interest.
