Section 41.2 Terminology and notation
- quadratic form
-
a multivariable polynomial formula so that each term has degree two; that is, if the variables are \(x_1,x_2,\dotsc,x_n\text{,}\) each term in the formula is of the form
\begin{equation*} a x_i x_j \text{,} \end{equation*}where each \(a\) is an arbitrary constant, and where \(i = j\) is allowed to produce a true quadratic term
- cross terms (in a quadratic formula)
mixed-variable terms of the form \(a x_i x_j \text{,}\) with \(i \neq j\)
- diagonal quadratic form
a quadratic form with no cross terms
- level set (at level \(k\) for a multivariable function \(f\))
the collection of points in \(\R^n\) that satisfy \(f(x_1,x_2,\dotsc,x_n) = k\text{;}\) also called a level curve for a piecewise-continuous function in two variables or a level surface for a piecewise-continuous function in three variables
- principal axes (for symmetric real matrix \(A\))
an orthonormal basis \(\basisfont{B}\) for \(\R^n\) so that the transition matrix \(\ucobmtrx{B}{S}\) orthogonally diagonalizes \(A\) (where \(\basisfont{S}\) is the standard basis)