  We show that modeling a Grassmannian as symmetric orthogonal matrices
$\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} :
Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} =
Q,\; \operatorname{tr}(Q)=2k - n\}$ yields exceedingly simple matrix formulas
for various curvatures and curvature-related quantities, both intrinsic and
extrinsic. These include Riemann, Ricci, Jacobi, sectional, scalar, mean,
principal, and Gaussian curvatures; Schouten, Weyl, Cotton, Bach, Pleba\'nski,
cocurvature, nonmetricity, and torsion tensors; first, second, and third
fundamental forms; Gauss and Weingarten maps; and upper and lower delta
invariants. We will derive explicit, simple expressions for the aforementioned
quantities in terms of standard matrix operations that are stably computable
with numerical linear algebra. Many of these aforementioned quantities have
never before been presented for the Grassmannian.
