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31 relations: Characteristic (algebra), Conic section, Derivative test, Diagonal matrix, Eigenvalues and eigenvectors, Ellipse, Ergebnisse der Mathematik und ihrer Grenzgebiete, Hyperbola, Invertible matrix, Isotropic quadratic form, Mathematical optimization, Mathematics, Matrix (mathematics), Matrix calculus, Minor (linear algebra), Norm (mathematics), Ordered field, Parabola, Polarization identity, Positive-definite function, Positive-definite matrix, Quadratic form, Real number, Regression analysis, Second partial derivative test, Sign (mathematics), Springer Science+Business Media, Symmetric bilinear form, Symmetric matrix, Transpose, Vector space.
Characteristic (algebra)
In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.
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Conic section
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
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Derivative test
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point.
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Diagonal matrix
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero.
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Eigenvalues and eigenvectors
In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.
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Ellipse
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
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Ergebnisse der Mathematik und ihrer Grenzgebiete
Ergebnisse der Mathematik und ihrer Grenzgebiete/A Series of Modern Surveys in Mathematics is a series of scholarly monographs published by Springer Science+Business Media.
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Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
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Invertible matrix
In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
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Isotropic quadratic form
In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero.
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Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Matrix (mathematics)
In mathematics, a matrix (plural: matrices) is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.
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Matrix calculus
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.
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Minor (linear algebra)
In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or more of its rows or columns.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Ordered field
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations.
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Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
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Polarization identity
In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space.
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Positive-definite function
In mathematics, a positive-definite function is, depending on the context, either of two types of function.
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Positive-definite matrix
In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.
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Quadratic form
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Regression analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships among variables.
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Second partial derivative test
In mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum, maximum or saddle point.
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Sign (mathematics)
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Symmetric bilinear form
A symmetric bilinear form on a vector space is a bilinear map from two copies of the vector space to the field of scalars such that the order of the two vectors does not affect the value of the map.
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Symmetric matrix
In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.
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Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
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Vector space
A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.
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References
[1] https://en.wikipedia.org/wiki/Definite_quadratic_form
