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Topic: Matrix representation of conic sections

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	Matrix representation of conic sections - Wikipedia, the free encyclopedia
		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.
		The major and minor axes are two lines determined by the center of the conic as a point and eigenvectors of the associated matrix as vectors of direction.
		As special cases, the center of a conic is the pole of the line at infinity, and each asymptote of a hyperbola is a polar (a tangent) to one of its points at infinity.
	en.wikipedia.org /wiki/Matrix_representation_of_conic_sections (518 words)

	Conic section
		In mathematics, a conic section is a two-dimensional curved locus of points, formed by the intersection of a cone and a plane.
		The degenerate cases, where the plane passes through the vertex of the cone, resulting in an intersection figure of a point, a straight line or a pair of lines, are not considered as conic sections.
		Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
	www.teachtime.com /en/wikipedia/c/co/conic_section.html (383 words)

	conic section - Article and Reference from OnPedia.com
		The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties.
		The semi-latus rectum of a conic section, usually denoted l, is the distance from the single focus, or one of the two foci, to the conic section itself, measured along a line perpendicular to the major axis.
		Note that this is the equation of the projection of the conic section on the xy-plane, hence contracted in the x-direction compared with the shape of the conic section itself.
	www.onpedia.com /encyclopedia/conic-section (1585 words)

	NationMaster - Encyclopedia: List of matrices
		Companion matrix - the companion matrix of a polynomial is a special form of matrix, whose eigenvalues are equal to the roots of the polynomial.
		Permutation matrix - matrix representation of a permutation.
		In the mathematical subfield of numerical analysis a sparse matrix is a matrix populated primarily with zeros.
	www.nationmaster.com /encyclopedia/List-of-matrices (3818 words)

	Conic section - Wikipedia, the free encyclopedia
		In mathematics, a conic section (or just conic) is a curve formed by intersecting a cone (more precisely, a right circular conical surface) with a plane.
		The degenerate cases, where the plane passes through the apex of the cone, resulting in an intersection figure of a point, a straight line, or a pair of intersecting lines, are often excluded from the list of conic sections.
		All conics have identical properties in projective space, and every theorem in projective geometry true of one conic section is true of all the others.
	en.wikipedia.org /wiki/Conic_sections (1618 words)

	Matrix representation of conic sections (Site not responding. Last check: 2007-10-21)
		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 point.
		The major and minor axes are two determined by the center of the conic a point and eigenvectors of the associated matrix as vectors direction.
		The reduced equation of a conic section is the equation of a conic translated and rotated so that its center in the center of the coordinate system its axes are parallel to the coordinate This is equivalent to saying that the are moved to satisfy these properties.
	www.freeglossary.com /Matrix_representation_of_conic_sections (545 words)

	Conic section (Site not responding. Last check: 2007-10-21)
		The conic sections were named and as long ago as 200 BC when Apollonius of Perga undertook a systematic study of their
		Conic sections are important in astronomy : the orbits of two massive objects that interact to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
		Note that this is the equation of projection of the conic section on the hence contracted in the x-direction compared with shape of the conic section itself.
	www.freeglossary.com /Conics (1692 words)

	Conic section - Term Explanation on IndexSuche.Com
		Conic sections are important in are conic sections if their common center_of_mass is considered to be at rest.
		In projective_geometry, the conic sections in the projective plane are equivalent to each other up_to projective_transformations.
		\qquad \qquad (3) Note that this is the equation of the projection of the conic section on the xy-plane, hence contracted in the x-direction compared with the shape of the conic section itself.
	www.indexsuche.com /Conic_section (1446 words)

	List of matrices (Site not responding. Last check: 2007-10-21)
		* Idempotent matrix — a matrix that has the property 'A' Identity matrix — a square diagonal matrix, with all entries on the main diagonal equal to 1, and the rest 0.
		* Skew-symmetric matrix — a matrix which is equal to the negative of its transpose, 'A' = −'A'.
		* Symmetric matrix — a square matrix which is equal to its transpose, 'A' = 'A' Symplectic matrix — a square matrix preserving a standard skew-symmetric form.
	www.paloweb.com /wikipedia.asp?l=en&pages=List+of+matrices (1072 words)

	Matrix representation of conic sections
		The matrix representation of conic sections is one way of studying a conic section, its axis, vertices, focuses, tangents, and the relative position of a given point.
		Because a 3x3 matrix has 2 eigenvectors, we obtain 2 axes.
		For a general conic we can determine its vertices by calculating the intersection of the conic and its axes#&8212;in other words, by solving the system:
	www.ebroadcast.com.au /lookup/encyclopedia/ma/Matrix_representation_of_conic_sections.html (444 words)

	Matrix representation of conic sections (Site not responding. Last check: 2007-10-21)
		In mathematics, the matrix representation of conicsections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point.
		Conic sections have the form of a second-degree polynomial :
		The reduced equation of a conic section is the equation of a conic section translated and rotated so that its centerlies in the center of the coordinate system and its axes are parallel to the coordinate axes.
	www.therfcc.org /matrix-representation-of-conic-sections-206483.html (299 words)

	Conic section: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-21)
		A parabola (from the greek:) is a conic section generated by the intersection of a cone, and a plane (mathematics)plane...
		In geometry, a nondegenerate conic section formed by a plane intersecting a cone has one or two dandelin spheres characterized thus:...
		In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, focus (geometry)foci, tangents,...
	www.absoluteastronomy.com /enc3/conic_section (2621 words)

	Facts about diagonal matrix (Site not responding. Last check: 2007-10-21)
		Any diagonal matrix is also a symmetric matrix, a triangular matrix, and (if the entries come from the field R or C) also a normal matrix.
		Because of the simple description of the matrix operation and eigenvalues/eigenvectors given above, it is always desirable to represent a given matrix or linear map by a diagonal matrix.
		Over the field of real or complex numbers, more is true: every normal matrix is unitarily similar to a diagonal matrix (the spectral theorem), and every matrix is unitarily equivalent to a diagonal matrix with nonnegative entries (the singular value decomposition).
	www.supercrawler.com /Facts/diagonal_matrix.html (269 words)

	Conic section - Gurupedia
		straight line or a pair of lines, are often excluded from the list of conic sections.
		orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
		Focus#Geometry of conic sections, an overview of properties of conic sections related to the foci.
	www.gurupedia.com /c/co/conic.htm (1187 words)

	Encyclopedia Search (Site not responding. Last check: 2007-10-21)
		.The set of all the eigenvalues is called the matrix or operator...
		...the center of the conic as a point and
		s of the associated matrix as vectors of direction.
	www.encyclopedian.com /search.php?searWords=Eigenvector (60 words)

	Conic Section (Site not responding. Last check: 2007-10-21)
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		When a cosmic muon passes through, the photomultipliers trace out a perfect ellipse or hyperbola (a conic section) on the wall.
	www.wikiverse.org /conic-section (1282 words)

	Conic section parameterization
		The conic curves are: ellipses, circles, parabolas, and hyperbolas.
		This transformation matrix M is found as a sequence of individual operations of rotation, translation and scaling.
		That conic section is the intersection of a plane through the vertex of the cone, (0,0,0), and results in a point (degenerate ellipse), line (degenerate parabola), or a pair of intersecting lines (degenerate hyperbola).
	science.gmu.edu /~jsteidel/806-prj/project.html (1765 words)

	List of matrices - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-10-21)
		Identity matrix - a square diagonal matrix, with all entries on the main diagonal equal to 1.
		Pick matrix - occurs in the study of analytical interpolation problems
		Unimodular matrix - a square matrix with determinant +1 or -1.
	encyclopedia.learnthis.info /l/li/list_of_matrices.html (622 words)

	Conic Sections - Personal (Site not responding. Last check: 2007-10-21)
		Our Conic Sections website is too advanced so we have not much managed to assistance lots of content, however what we have done so far is researched the too best Conic Sections sites on the net.
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	personal.best-resource-links-13.info /Blaise_Pascal/Conic_sections (1094 words)

	Matrix Distinctive (Site not responding. Last check: 2007-10-21)
		She examines Morrison's facility with imagery Matrix Distinctive and wordplay Matrix Distinctive and discusses the ways in which Morrison contends with the expectations of gender Matrix Distinctive and race that have stiffened into traditions--or worse, prejudices.
		See live article Vandermonde matrix In linear algebra, a Vandermonde matrix is a matrix with a geometric progression in each column, i.e; In mathematical terms: These matrices are useful in polynomial interpolation, since solving an equation for, is equivalent to finding the coefficents of a polynomial that has values...
		A Hermitian matrix is a square matrix with complex that is equal to its own conjugate transpose - that is, if the element in the ith row and jth column is equal to the complex conjugate of...
	www.barkerverse.com /70/21.html (1146 words)

	ipedia.com: Conic section Article (Site not responding. Last check: 2007-10-21)
		In mathematics, a conic section is a curved locus of points, formed by intersecting a cone with a plane.
		The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga under...
		works which give detailed account, in alphabetical order, of whole field of human knowledge, or of some particular section in it.
	www.ipedia.com /conic_section.html (1244 words)

	Matrix representation of conic sections - TheBestLinks.com - Conic section, Determinant, Eigenvectors, Ellipse, ... (Site not responding. Last check: 2007-10-21)
		Matrix representation of conic sections - TheBestLinks.com - Conic section, Determinant, Eigenvectors, Ellipse,...
		Matrix representation of conic sections, Conic section, Determinant...
		\left\{\begin{matrix} and e and\qquad \mbox{(axis)} \\ and Q and\qquad \mbox{(the general equation of the conic)} \end{matrix} \right.
	www.thebestlinks.com /Matrix_representation_of_conic_sections.html (515 words)

	Matrix Reduced (Site not responding. Last check: 2007-10-21)
		See live article Matrix representation of conic sections 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.
		Table of contents showTocToggle("show","hide") 1 Set theoretic representation 2 Linear representation 2.1 Example 2.2 Equivalence of representations 2.3 Group actions 2.4 Reducibility 2.5 Character theory Set theoretic representation A set S is said to be a set-theoretic representation of a group G if there is a function, from G to...
		For example, the representation of C3 given by the matrices: is an equivalent representation to the one shown above.
	www.barkerverse.com /70/66.html (1236 words)

	Conic section (Site not responding. Last check: 2007-10-21)
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	www.omniknow.com /common/wiki.php?in=en&term=Directrix (2871 words)

	The Matrix
		The Matrix is a film first released in the USA on March 31, 1999, written and directed by the Wachowski brothers (Andy and Larry).
		The film describes a world in which the titular Matrix is an artificial reality created by sentient machines in order to pacify and subdue the human population.
		It contains numerous references to philosophical and religious ideas, and to the hacker subculture, as well as homages to the style of Japanese animation and cyberpunk.
	www.kiwipedia.com /en/the-matrix.html (146 words)

	NationMaster - Encyclopedia: Dandelin spheres
		Each conic section has one Dandelin sphere for each focus.
		An ellipse has two Dandelin spheres, both touching the same nappe of the cone.
		The point at which the sphere touches the plane is a focus of the conic section.
	www.nationmaster.com /encyclopedia/Dandelin-spheres (525 words)

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