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For central conics, both eigenvalues are non-zero and the classification of the conic sections can be obtained by examining them. If λ 1 and λ 2 have the same algebraic sign, then Q is a real ellipse, imaginary ellipse or real point if K has the same sign, has the opposite sign or is zero, respectively.
The Armed Services Vocational Aptitude Battery ( ASVAB) is a multiple choice test, administered by the United States Military Entrance Processing Command, used to determine qualification for enlistment in the United States Armed Forces. It is often offered to U.S. high school students when they are in the 10th, 11th and 12th grade, though ...
The discriminant B 2 – 4AC of the conic section's quadratic equation (or equivalently the determinant AC – B 2 /4 of the 2 × 2 matrix) and the quantity A + C (the trace of the 2 × 2 matrix) are invariant under arbitrary rotations and translations of the coordinate axes, [14] [15] [16] as is the determinant of the 3 × 3 matrix above.
In geometry, Poncelet's closure theorem, also known as Poncelet's porism, states that whenever a polygon is inscribed in one conic section and circumscribes another one, the polygon must be part of an infinite family of polygons that are all inscribed in and circumscribe the same two conics. [1] [2] It is named after French engineer and ...
Toeplitz matrix. In linear algebra, a Toeplitz matrix or diagonal-constant matrix, named after Otto Toeplitz, is a matrix in which each descending diagonal from left to right is constant. For instance, the following matrix is a Toeplitz matrix: Any matrix of the form. is a Toeplitz matrix. If the element of is denoted then we have.
Conic constant. In geometry, the conic constant (or Schwarzschild constant, [1] after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by where e is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is ...
Voronoi diagram. In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. It can be classified also as a tessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called ...
From January 2008 to December 2012, if you bought shares in companies when M. Anthony Burns joined the board, and sold them when he left, you would have a 10.2 percent return on your investment, compared to a -2.8 percent return from the S&P 500.