2.2.5 Polynomials

2.2.5  Polynomials

A polynomial from to is linear if it has form

[2.8]

with a and b scalars. It is quadratic if it has form:

[2.9]

with a, b and c scalars. These notions generalize to higher dimensions. A polynomial from n to is linear if it has form

[2.10]

with b an n-dimensional row vector and a a scalar. It is quadratic if it has form

[2.11]

with c an n×n matrix, b an n-dimensional row vector and a a scalar. Without loss of generality, we always assume c is symmetric. For example, the quadratic polynomial

[2.12]

can be expressed in form [2.11] with

[2.13]

[2.14]

[2.15]