quadric expression - definition. What is quadric expression
Diclib.com
قاموس ChatGPT
أدخل كلمة أو عبارة بأي لغة 👆
اللغة:

ترجمة وتحليل الكلمات عن طريق الذكاء الاصطناعي ChatGPT

في هذه الصفحة يمكنك الحصول على تحليل مفصل لكلمة أو عبارة باستخدام أفضل تقنيات الذكاء الاصطناعي المتوفرة اليوم:

  • كيف يتم استخدام الكلمة في اللغة
  • تردد الكلمة
  • ما إذا كانت الكلمة تستخدم في كثير من الأحيان في اللغة المنطوقة أو المكتوبة
  • خيارات الترجمة إلى الروسية أو الإسبانية، على التوالي
  • أمثلة على استخدام الكلمة (عدة عبارات مع الترجمة)
  • أصل الكلمة

%ما هو (من)٪ 1 - تعريف

LOCUS OF ZEROS OF A QUADRATIC POLYNOMIAL (AFFINE OR PROJECTIVE, NOT NECESSARILY REAL)
Quadric surface; Quadric (projective geometry); Quadric (Projective Geometry); Quadratic surface; Quadric hypersurface; Hyperbolic quadric; Quadric cone; Quadratic hypersurface; Quadrics

Quadric         
·adj Of or pertaining to the second degree.
II. Quadric ·noun A quantic of the second degree. ·see Quantic.
III. Quadric ·noun A surface whose equation in three variables is of the second degree. Spheres, spheroids, ellipsoids, paraboloids, hyperboloids, also cones and cylinders with circular bases, are quadrics.
quadric         
['kw?dr?k]
¦ adjective Geometry denoting a surface or curve described by an equation of the second degree.
Origin
C19: from L. quadra 'square' + -ic.
Expression (mathematics)         
FORMULA THAT REPRESENTS A MATHEMATICAL OBJECT
Mathematical expression; Expression (math); Compound expression; Algebraical quantity; Arithmetic expression; Finite expression; Mathematical expressions; Numeric expression
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

ويكيبيديا

Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections. When the defining polynomial is not absolutely irreducible, the zero set is generally not considered a quadric, although it is often called a degenerate quadric or a reducible quadric.

In coordinates x1, x2, ..., xD+1, the general quadric is thus defined by the algebraic equation

i , j = 1 D + 1 x i Q i j x j + i = 1 D + 1 P i x i + R = 0 {\displaystyle \sum _{i,j=1}^{D+1}x_{i}Q_{ij}x_{j}+\sum _{i=1}^{D+1}P_{i}x_{i}+R=0}

which may be compactly written in vector and matrix notation as:

x Q x T + P x T + R = 0 {\displaystyle xQx^{\mathrm {T} }+Px^{\mathrm {T} }+R=0\,}

where x = (x1, x2, ..., xD+1) is a row vector, xT is the transpose of x (a column vector), Q is a (D + 1) × (D + 1) matrix and P is a (D + 1)-dimensional row vector and R a scalar constant. The values Q, P and R are often taken to be over real numbers or complex numbers, but a quadric may be defined over any field.

A quadric is an affine algebraic variety, or, if it is reducible, an affine algebraic set. Quadrics may also be defined in projective spaces; see § Normal form of projective quadrics, below.