Linear Polynomial, Quadratic Polynomial

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	Ads by Contingency Analysis

A polynomial from to is linear if it has form

p(x) = bx + a

[1]

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

p(x) = cx² + bx + a

[2]

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

p(x) = bx + a

[3]

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

[4]

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

[5]

can be expressed in form [4] with

	[6]
b = ( 0 1 0 )	[7]
a = 17	[8]