A squared linear function is a quadratic function [latex]q: \mathbb{R}^n \rightarrow \mathbb{R}[/latex] of the form

[latex]\begin{align*} q(x) &= (v^Tx)^2, \end{align*}[/latex]

for some vector [latex]v \in \mathbb{R}^n[/latex].

The function vanishes on the space orthogonal to [latex]v[/latex], which is the hyperplane defined by the single linear equation [latex]v^Tx = 0[/latex]. Thus, in effect this function is really one-dimensional: it varies only along the direction [latex]v[/latex].

	Level sets and graph of a dyadic quadratic function, corresponding to the vector [latex]v= (2,1)[/latex]. The function is constant along hyperplanes orthogonal to [latex]v[/latex].