Definition of Principal axes of a quadric. Meaning of Principal axes of a quadric. Synonyms of Principal axes of a quadric

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Definition of Principal axes of a quadric

Principal axes of a quadric
Principal Prin"ci*pal, a. [F., from L. principalis. See Prince.] 1. Highest in rank, authority, character, importance, or degree; most considerable or important; chief; main; as, the principal officers of a Government; the principal men of a state; the principal productions of a country; the principal arguments in a case. Wisdom is the principal thing. --Prov. iv. 7. 2. Of or pertaining to a prince; princely. [A Latinism] [Obs.] --Spenser. Principal axis. See Axis of a curve, under Axis. Principal axes of a quadric (Geom.), three lines in which the principal planes of the solid intersect two and two, as in an ellipsoid. Principal challenge. (Law) See under Challenge. Principal plane. See Plane of projection (a), under Plane. Principal of a quadric (Geom.), three planes each of which is at right angles to the other two, and bisects all chords of the quadric perpendicular to the plane, as in an ellipsoid. Principal point (Persp.), the projection of the point of sight upon the plane of projection. Principal ray (Persp.), the line drawn through the point of sight perpendicular to the perspective plane. Principal section (Crystallog.), a plane passing through the optical axis of a crystal.

Meaning of Principal axes of a quadric from wikipedia

- In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and...
- degenerate quadric surfaces. When the prin****l axes of a quadric are aligned with the reference frame (always possible for a quadric), a general equation of the...
- center of the ellipsoid. The line segments that are delimited on the axes of symmetry by the ellipsoid are called the prin****l axes, or simply axes of the...
- called a transformation of coordinates. The solutions to many problems can be simplified by translating the coordinate axes to obtain new axes parallel...
- same axes and if their intersections with each plane of symmetry are confocal conics. Analogous to conics, nondegenerate pencils of confocal quadrics come...
- locus of points that represent the state of stress on individual planes at all their orientations, where the axes represent the prin****l axes of the stress...
- transformation. A hyperboloid is a quadric surface, that is, a surface defined as the zero set of a polynomial of degree two in three variables. Among quadric surfaces...
- to also include representations of some non-spherical entities: prin****l axes-aligned quadric surfaces and many of their degenerate forms such as planes...
- A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its prin****l...
- Originally used to study prin****l axes of the rotational motion of rigid bodies, eigenvalues and eigenvectors have a wide range of applications, for example...