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A real symmetric matrix whose quadratic form is positive at every nonzero vector in the nonnegative orthant. By compactness of the nonnegative unit sphere, this is equivalent to a positive uniform lower bound $x^{T}Ax\ge \delta \Vert x{\Vert }_2^2$ on that orthant. It need not be a positive-definite matrix.

A matrix is strictly diagonally dominant when every diagonal-dominance inequality is strict. A real symmetric strictly diagonally dominant matrix with positive diagonal is positive definite by the Gershgorin circle theorem.

Here $\mathbf{F},\mathbf{G}$ are forces and torques exerted by the body on the fluid, or the external force and torque needed to maintain its motion. The Lorentz reciprocal theorem for Stokes flow makes the six-dimensional hydrodynamic resistance matrix symmetric. The power identity $\mathbf{F}\cdot \mathbf{U}+\mathbf{G}\cdot \mathbf{\Omega }=2\mu \int e:edV$ makes it a positive-definite matrix for a body moving in otherwise stationary unbounded fluid.

For unknown drift $X\beta$, a full-column-rank design matrix $X$, a known positive-definite matrix observation covariance matrix $\Sigma$, and target drift row $x_0^T$, universal kriging minimizes prediction variance subject to $X^{T}w=x_0$. Equivalently, with $\hat{\beta }=(X^T{\Sigma }^{-1}X{)}^{-1}{X}^T{\Sigma }^{-1}z$, predict $x_0^T\hat{\beta }+c^T{\Sigma }^{-1}(z-X\hat{\beta })$. The first term is the estimated trend alone; the second is a correlated residual prediction.