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For a design matrix $X$ with $p$ columns, define ${\kappa }_m^2={\max }_{|M|=m}{\lambda }_{\max }(X_M^T{X}_M/n)$ for $1\le m\le p$. Equivalently this bounds $\Vert Xv{\Vert }_2^2/(n\Vert v{\Vert }_2^2)$ for vectors supported on at most $m$ coordinates. These quantities are nondecreasing: extend the support of a maximizing vector by zero coordinates and use the variational characterization of the largest eigenvalue. Values at $m>p$, including infinity, require a separate convention.

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.