Matrix Representation of Conic Sections | Matrix Representation Conic Sections

In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes aren't parallel to our coordinate system.

Conic sections have the form of a second-degree polynomial:

$Q \ \stackrel{\mathrm{def}}{=}\ Ax^2+Bxy+Cy^2+Dx+Ey+F=0. \,$

That can be written as:

$\mathbf{x}^T A_Q\mathbf{x}=0$

Where is the homogeneous coordinate vector:

$\begin{pmatrix} x \\ y \\ 1 \end{pmatrix}$

And a matrix:

$A_Q = \begin{pmatrix} A & B/2 & D/2 \\ B/2 & C & E/2 \\ D/2 & E/2 & F \end{pmatrix}.$

Read more about Matrix Representation Of Conic Sections: Classification, Center, Axes, Vertices, Tangents, Reduced Equation

Famous quotes containing the words matrix and/or sections:

““The matrix is God?”
“In a manner of speaking, although it would be more accurate ... to say that the matrix has a God, since this being’s omniscience and omnipotence are assumed to be limited to the matrix.”
“If it has limits, it isn’t omnipotent.”
“Exactly.... Cyberspace exists, insofar as it can be said to exist, by virtue of human agency.””
—William Gibson (b. 1948)

“Childhood lasts all through life. It returns to animate broad sections of adult life.... Poets will help us to find this living childhood within us, this permanent, durable immobile world.”
—Gaston Bachelard (1884–1962)