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  2. Discriminant - Wikipedia

    en.wikipedia.org/wiki/Discriminant

    The discriminant of a polynomial of degree n is homogeneous of degree 2n − 2 in the coefficients. This can be seen in two ways. In terms of the roots-and-leading-term formula, multiplying all the coefficients by λ does not change the roots, but multiplies the leading term by λ.

  3. Discriminant of an algebraic number field - Wikipedia

    en.wikipedia.org/wiki/Discriminant_of_an...

    An integer that occurs as the discriminant of a quadratic number field is called a fundamental discriminant. [3] Cyclotomic fields: let n > 2 be an integer, let ζ n be a primitive nth root of unity, and let K n = Q(ζ n) be the nth cyclotomic field. The discriminant of K n is given by [2] [4]

  4. Hessian matrix - Wikipedia

    en.wikipedia.org/wiki/Hessian_matrix

    This "part" is the so-called complex Hessian, which is the matrix (¯),. Note that if f {\displaystyle f} is holomorphic, then its complex Hessian matrix is identically zero, so the complex Hessian is used to study smooth but not holomorphic functions, see for example Levi pseudoconvexity .

  5. Glossary of algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_algebraic_geometry

    This is a glossary of algebraic geometry. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory. For the number-theoretic applications, see glossary of arithmetic and Diophantine geometry.

  6. Determinant - Wikipedia

    en.wikipedia.org/wiki/Determinant

    The above formula shows that its Lie algebra is the special linear Lie algebra consisting of those matrices having trace zero. Writing a 3 × 3 {\displaystyle 3\times 3} -matrix as A = [ a b c ] {\displaystyle A={\begin{bmatrix}a&b&c\end{bmatrix}}} where a , b , c {\displaystyle a,b,c} are column vectors of length 3, then the gradient over one ...

  7. Resultant - Wikipedia

    en.wikipedia.org/wiki/Resultant

    In some older texts, the resultant is also called the eliminant. [1] The resultant is widely used in number theory, either directly or through the discriminant, which is essentially the resultant of a polynomial and its derivative. The resultant of two polynomials with rational or polynomial coefficients may be computed efficiently on a computer.

  8. Jacobian matrix and determinant - Wikipedia

    en.wikipedia.org/wiki/Jacobian_matrix_and...

    Specifically, if the eigenvalues all have real parts that are negative, then the system is stable near the stationary point. If any eigenvalue has a real part that is positive, then the point is unstable. If the largest real part of the eigenvalues is zero, the Jacobian matrix does not allow for an evaluation of the stability. [12]

  9. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    3. Between two groups, may mean that the first one is a proper subgroup of the second one. > (greater-than sign) 1. Strict inequality between two numbers; means and is read as "greater than". 2. Commonly used for denoting any strict order. 3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1.