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Index of articles associated with the same name
mathematics, negative definiteness is a property of any object to which a bilinear form may be naturally associated, which is negative-definite. See, in particular:
Negative_definiteness
Property of a mathematical matrix
semi-definite and not negative semi-definite is sometimes called indefinite. Some authors use more general definitions of definiteness, permitting the matrices to
Definite_matrix
Type of homogeneous polynomial of degree 2
involving products of two different variables. Positive or negative-definiteness or semi-definiteness, or indefiniteness, of this quadratic form is equivalent
Definite_quadratic_form
Concept in quantum mechanics
counterfactual definiteness (CFD) is an open question in quantum mechanics. Whether experts working in the field can speak "meaningfully" of the definiteness of the
Counterfactual_definiteness
Word used with a noun to indicate the type of reference being made by the noun
the grammatical definiteness of the noun phrase. In English, the and a (rendered as an when followed by a vowel sound) are the definite and indefinite
Article_(grammar)
Bimodal function
linear. Positive-definiteness arises naturally in the theory of the Fourier transform; it can be seen directly that to be positive-definite it is sufficient
Positive-definite_function
Method in multivariable calculus
the signs of these minors are the conditions for the positive or negative definiteness of the Hessian. For the general case of an arbitrary number n of
Second partial derivative test
Second_partial_derivative_test
Matrix of second derivatives
positive-definite at x , {\displaystyle x,} then f {\displaystyle f} attains an isolated local minimum at x . {\displaystyle x.} If the Hessian is negative-definite
Hessian_matrix
Mathematical function often applied to matrices
induced operator norm. It quantifies key notions such as positive/negative definiteness in matrix theory, uniformly coercive or monotone vector fields in
Logarithmic_norm
On when a definite intersection form of a smooth 4-manifold is diagonalizable
a definite intersection form of a closed, oriented, smooth manifold of dimension 4 is diagonalizable. If the intersection form is positive (negative) definite
Donaldson's_theorem
Generalization of a positive-definite matrix
F . {\displaystyle K(x,y)=(\Phi (x),\Phi (y))_{F}.} Indeed, positive definiteness of K {\displaystyle K} follows from the p.d. property of the inner product
Positive-definite_kernel
Symmetric bilinear form in mathematics
a compact Lie group. The definition of compactness in terms of negative definiteness of the Killing form is more restrictive, since using this definition
Killing_form
Concept in the analysis of dynamical systems
{V}\cdot g} is locally positive definite, or ∇ V ⋅ g {\displaystyle \nabla {V}\cdot g} is locally negative definite. Lyapunov functions arise in the
Lyapunov_function
Polynomial with all terms of degree two
positive definite if q(v) > 0 (similarly, negative definite if q(v) < 0) for every nonzero vector v. When q(v) assumes both positive and negative values
Quadratic_form
one-dimensional subspace, and a complementary subspace on which it is negative definite. In a more formal statement, specify that V is a non-singular projective
Hodge_index_theorem
Vector on which a quadratic form is zero
orthogonal subspaces A and B, X = A + B, where q is positive-definite on A and negative-definite on B. The null cone, or isotropic cone, of X consists of
Null_vector
Grammatical category indicating truth or falsehood
aff) and negation (neg) are ways in which grammar encodes positive and negative polarity into verb phrases, clauses, or utterances. An affirmative (positive)
Affirmation_and_negation
Isolated point in the solution set of a polynomial equation in two real variables
Further the Hessian matrix of second derivatives will be positive definite or negative definite, since the function must have a local minimum or a local maximum
Acnode
Words in Bulgarian that substitute for a noun or noun phrase
number, definiteness and case. Pronouns are classified as: personal, possessive, interrogative, demonstrative, reflexive, universal, negative, indefinite
Pronouns_in_Bulgarian
Statistical model
completely defines the process' behaviour. Importantly the non-negative definiteness of this function enables its spectral decomposition using the Karhunen–Loève
Gaussian_process
Definite article in English
otherwise presumed familiar to listeners, readers, or speakers. It is the only definite article in English. The is the most frequently used word in the English
The
In mathematics, a linear operator acting on inner product space
acting on an inner product space is called positive-semidefinite (or non-negative) if, for every x ∈ Dom ( A ) {\displaystyle x\in \operatorname {Dom}
Positive_operator
Mathematical theory
is negative semidefinite, not negative definite in general. If the Killing form of a Lie algebra is negative definite, then the Lie algebra is the Lie
Compact_Lie_algebra
Fourier transform of the probability density function
usefulness is limited because the main condition of the theorem, non-negative definiteness, is very hard to verify. Other theorems also exist, such as Khinchine’s
Characteristic function (probability theory)
Characteristic_function_(probability_theory)
Distance from zero to a number
used for generalization of this notion to other domains: Non-negativity, positive definiteness, and multiplicativity are readily apparent from the definition
Absolute_value
Mathematical function
argument of the exponential function in the Gaussian function is any negative-definite quadratic form. Consequently, the level sets of the Gaussian will
Gaussian_function
Computational physics simulation tool
non-negative definite and bounded: 0 ≤ Q ( α ) ≤ 1 π . {\displaystyle 0\leq Q(\alpha )\leq {\frac {1}{\pi }}.} Despite the fact that Q is non-negative definite
Husimi_Q_representation
Method of data analysis
. This is very constructive, as cov(X) is guaranteed to be a non-negative definite matrix and thus is guaranteed to be diagonalisable by some unitary
Principal_component_analysis
Family of implicit and explicit iterative methods
both non-negative definite. A sufficient condition for B-stability is: B {\displaystyle B} and Q {\displaystyle Q} are non-negative definite. In general
Runge–Kutta_methods
Theorem of matrix algebra of invariance properties under basis transformations
form is positive definite (respectively, negative definite) have the same dimension. These dimensions are the positive and negative indices of inertia
Sylvester's_law_of_inertia
Array of numbers
\mathbb {R} ^{n}} . If f(x) yields only negative values then A is negative-definite; if f does produce both negative and positive values then A is indefinite
Matrix_(mathematics)
Algebra based on a vector space with a quadratic form
Cl0,n(R), depending on whether the author prefers positive-definite or negative-definite spaces. A standard basis {e1, ..., en} for Rp,q consists of
Clifford_algebra
1932 book by John von Neumann
by noting that ρ {\displaystyle \rho } must be Hermitian and non-negative definite ( ⟨ ρ ⟩ ≥ 0 {\displaystyle \langle \rho \rangle \geq 0} ) by construction
Mathematical Foundations of Quantum Mechanics
Mathematical_Foundations_of_Quantum_Mechanics
Property of a dynamical system where solutions near an equilibrium point remain so
{\displaystyle A} are negative. This condition is equivalent to the following one: A T M + M A {\displaystyle A^{\textsf {T}}M+MA} is negative definite for some positive
Lyapunov_stability
Statistical distribution of complex random variables
covariance matrix Γ {\displaystyle \Gamma } is Hermitian and non-negative definite; and, the relation matrix or pseudo-covariance matrix C {\displaystyle
Complex_normal_distribution
Analyzes the topology of a manifold by studying differentiable functions on that manifold
{\displaystyle p} on which the Hessian of f {\displaystyle f} is negative definite. The indices of basins, passes, and peaks are 0 , 1 , {\displaystyle
Morse_theory
Statistical technique
indicates that a square symmetric matrix A {\displaystyle A} is non-negative definite. Consequently, any given linear form of the PCR estimator has a lower
Principal component regression
Principal_component_regression
Study of mathematical algorithms for optimization problems
critical points can be classified using the definiteness of the Hessian matrix: If the Hessian is positive definite at a critical point, then the point is
Mathematical_optimization
Operation in calculus
above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an antiderivative, a function whose
Integral
Smooth 4-manifold homeomorphic yet not diffeomorphic to Euclidean space
intersection form − E 8 ⊕ [ − 1 ] {\displaystyle -E_{8}\oplus [-1]} being negative definite and not diagonalizable, which Donaldson's theorem forbids if it was
Exotic_R4
arrows. A real Lie algebra g0 is called compact if the Killing form is negative definite, i.e. the index of g0 is zero. In this case g0 = k0 is a compact Lie
Real_form_(Lie_theory)
Matrix with the same number of rows and columns
eigenvalues are real. A symmetric n×n-matrix is called positive-definite (respectively negative-definite; indefinite), if for all nonzero vectors x ∈ R n {\displaystyle
Square_matrix
Solving an optimization problem with a quadratic objective function
x , λ ) = 0 {\displaystyle \nabla _{x}L(x,\lambda )=0} and positive-definiteness of Q: x ∗ = − Q − 1 A ⊤ λ . {\displaystyle x^{*}=-Q^{-1}A^{\top }\lambda
Quadratic_programming
Concepts from linear algebra
is not only Hermitian but also positive-definite, positive-semidefinite, negative-definite, or negative-semidefinite, then every eigenvalue λ i {\displaystyle
Eigenvalues_and_eigenvectors
Mathematical theorem
between positive definiteness and harmonic analysis, providing a stronger and more direct characterization of positive definiteness than the abstract
Mercer's_theorem
Concept in science
of the outcome of an experiment is never negative, although a quasiprobability distribution allows a negative probability, or quasiprobability for some
Negative_probability
First-order differential linear operator on spinor bundle, whose square is the Laplacian
_{j=1}^{n}\left({\frac {\partial }{\partial x_{j}}}\right)^{2}{,}} which is negative-definite, in the sense that ∫ R n φ ( x ) ¯ Δ φ ( x ) d x = − ∫ R n | ∇ φ (
Dirac_operator
Distance between probability distributions
Y')].} This is not necessarily non-negative, however. If ( M , d ) {\displaystyle (M,d)} is a strongly negative definite kernel, then D {\displaystyle D}
Energy_distance
Mathematical function for the probability a given outcome occurs in an experiment
of the beta distribution Wishart distribution, for a symmetric non-negative definite matrix; conjugate to the inverse of the covariance matrix of a multivariate
Probability_distribution
Number of positive, negative and zero eigenvalues of a metric tensor
vector subspace on which the scalar product g is positive-definite (resp. negative-definite), and r is the dimension of the radical of the scalar product
Metric_signature
Generalized matrix decomposition for Lie groups and Lie algebras
decomposition is that the Killing form is negative definite on k {\displaystyle {\mathfrak {k}}} and positive definite on p {\displaystyle {\mathfrak {p}}}
Cartan_decomposition
so that the time derivative of the system's Lyapunov function is negative definite at that point. In other words, even if the control input is arbitrarily
Small_control_property
Point where the derivative of a function is zero or undefined (in certain cases)
Hessian matrix is negative definite; it is a local minimum if the index is zero, or, equivalently, if the Hessian matrix is positive definite. For the other
Critical_point_(mathematics)
English mathematician (born 1957)
of a smooth, closed, simply connected 4-manifold is positive- or negative-definite then it is diagonalizable over the integers. This result is sometimes
Simon_Donaldson
Automobiles notable for negative reception
Some models of automobiles receive high positive acclaim or negative reviews in the media and trade magazines. Reviews are both subjective and performance-based
List of automobiles notable for negative reception
List_of_automobiles_notable_for_negative_reception
Method of estimating the parameters of a statistical model, given observations
_{k}^{2}}}\right|_{\theta ={\widehat {\theta \,}}}\end{bmatrix}}~,} is negative semi-definite at θ ^ {\displaystyle {\widehat {\theta \,}}} , as this indicates
Maximum_likelihood_estimation
Concept in theory of differential equations
stable. If V ˙ ( x ) {\displaystyle {\dot {V}}(\mathbf {x} )} is negative definite, then the global asymptotic stability of the origin is a consequence
LaSalle's invariance principle
LaSalle's_invariance_principle
Differentiable manifold with nondegenerate metric tensor
generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a
Pseudo-Riemannian_manifold
Method for approximate evaluation of integrals
Analogously to the univariate case, the Hessian is required to be negative-definite. In extensions of Laplace's method, complex analysis, and in particular
Laplace's_method
Theorem describing translation of Gaussian measures on Hilbert spaces
p. 280) that for a q × q {\displaystyle q\times q} symmetric non-negative definite matrix H ( t ) {\displaystyle H(t)} whose elements H j , k ( t ) {\displaystyle
Cameron–Martin_theorem
Quadratic homogeneous polynomial in two variables
and negative if a < 0 {\displaystyle a<0} . For this reason, the former are called positive definite forms and the latter are negative definite. The
Binary_quadratic_form
Maximally symmetric Lorentzian manifold with a negative cosmological constant
space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analogue of hyperbolic space. Anti-de Sitter
Anti-de_Sitter_space
Mathematical term in calculus
value is a logarithm. For negative values of n (negative powers of x), there is a singularity at x = 0, and thus the definite integral is based at 1, rather
Cavalieri's quadrature formula
Cavalieri's_quadrature_formula
Modern Jewish-Aramaic dialect of Iraq
to a noun, the singular and plural endings -a and -e are taken off. Definiteness is expressed if the speaker assumes the hearer has background knowledge
Inter-Zab_Jewish_Neo-Aramaic
Application of Lagrangian mechanics to field theories
vector. More precisely, they are positive definite for mostly negative metric signatures, and negative-definite for mostly positive metric signatures. This
Lagrangian_(field_theory)
Space in mathematics and theoretical physics
U, following three cases are possible: q|U is either positive or negative definite. Then, U is essentially Euclidean (up to the sign of q). q|U is indefinite
Pseudo-Euclidean_space
Spatial statistics function
function is a semivariogram if and only if it is a conditionally negative definite function, i.e. for all weights w 1 , … , w N {\displaystyle w_{1}
Variogram
Function related to statistics and probability theory
_{j}}}\,\right]_{i,j=1,1}^{n_{\mathrm {i} },n_{\mathrm {j} }}\;} is negative definite for every θ ∈ Θ {\textstyle \theta \in \Theta } at which the gradient
Likelihood_function
Manifold union
tangent space T p j M {\displaystyle T_{p_{j}}M} where the Hessian is negative definite. Provided the indices satisfy I ( 1 ) ≤ I ( 2 ) ≤ ⋯ ≤ I ( k ) {\displaystyle
Handle_decomposition
Lie algebra, usually infinite-dimensional
Since the diagonal entries of C and D are positive, S cannot be negative definite or negative semidefinite. Symmetrizable indecomposable generalized Cartan
Kac–Moody_algebra
English words "the", "a(n)", and sometimes "some"
the articles the and a(n), which specify the presence or absence of definiteness of the noun. Other possible determiners include words like this, my,
English_articles
(pseudo-)Riemannian manifold whose geodesics are reversible
Killing form. The minus sign appears because the Killing form is negative-definite on h ; {\displaystyle {\mathfrak {h}}~;} this makes ⟨ ⋅ , ⋅ ⟩ g
Symmetric_space
Direct sum of simple Lie algebras
A real form is called a compact form if the Killing form on it is negative-definite; it is necessarily the Lie algebra of a compact Lie group (hence,
Semisimple_Lie_algebra
Algebraic variety of dimension two
intersection form to { H } ⊥ {\displaystyle \{H\}^{\perp }} is a negative definite quadratic form. This theorem is proven using the Nakai criterion and
Algebraic_surface
Type of group in mathematics
two maximal subspaces where the quadratic form is positive definite or negative definite. The component of the identity, whose elements preserve orientation
Orthogonal_group
Cushitic language of Northeast Africa
noun phrases. They agree in gender, number, case, and definiteness, and carry case and definiteness markers of the same form as nouns. Clauses may be composed
Beja_language
Determiners in the English language
"the most basic expression of definiteness and indefiniteness." That is, while other determiners express definiteness and other kinds of meaning, articles
English_determiners
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
is the signature of an invariant symmetric bilinear form that is negative definite on the maximal compact subgroup. It is equal to the dimension of the
Simple_Lie_group
Differential equation exhibiting high rate of dissipation
\Rightarrow \,\|R(hA)\|_{2}\leq 1\,,} i.e., if A {\displaystyle A} is negative definite, then the method produces a contractive recursion. (This is a variant
Stiff_equation
Correspondence between topics in Lie theory
subgroup. The Killing form on g {\displaystyle {\mathfrak {g}}} is negative definite. For each X in g {\displaystyle {\mathfrak {g}}} , ad ( X ) {\displaystyle
Lie group–Lie algebra correspondence
Lie_group–Lie_algebra_correspondence
Theorem in mathematics
b)} such that D ′ ( c ) = 0 {\displaystyle D'(c)=0} . Let X and Y be non-negative random variables such that E[X] < E[Y] < ∞ and X ≤ s t Y {\displaystyle
Mean_value_theorem
it's positive definite and # b 2 − ( M ) C P 2 ¯ {\displaystyle \#b_{2}^{-}(M){\overline {\mathbb {C} P^{2}}}} if it's negative definite. Proof: According
Freedman_classification
Elementary particle with negative charge
in nuclear reactions) is a subatomic particle whose electric charge is negative one elementary charge. It is an elementary particle contained in the matter
Electron
A negative pregnant (sometimes called a pregnant denial) refers to a denial which implies its affirmative opposite by seeming to deny only a qualification
Negative_pregnant
Ethio-Semitic language
is related to the definiteness of the object, thus Amharic shows differential object marking. In general, if the object is definite, possessed, or a proper
Amharic
Vector space in functional analysis
positive (negative) definite. A subspace in any of the above categories may be called semi-definite, and any subspace that is not semi-definite is called
Indefinite inner product space
Indefinite_inner_product_space
positive definite; if Δ < 0 {\displaystyle \Delta <0} and α < 0 {\displaystyle \alpha <0} then Q ( x , y ) {\displaystyle Q(x,y)} is said to be negative definite;
Gauss_composition_law
Influence one language has on the acquisition or intelligibility of another
language interference is most often discussed as a source of errors known as negative transfer, which can occur when speakers and writers transfer items and
Language_transfer
Matrix with no negative elements
positive-definite matrices, which are different. A matrix which is both non-negative and is positive semidefinite is called a doubly non-negative matrix
Nonnegative_matrix
Aspect of field theory
They have to be hermitian to give a real Lagrangian and positive-definite to avoid negative energy modes and instabilities, and to preserve unitarity. Unitarity
Kinetic_term
Manifold with inversion symmetry
a simple real Lie algebra g {\displaystyle {\mathfrak {g}}} with negative definite Killing form. It must admit an action of SU(2) which only acts via
Hermitian_symmetric_space
Device to trip a circuit breaker when a fault is detected
numerical relays can be used to provide inverse time overvoltage protection or negative sequence overcurrent protection. Ir = is the ratio of the fault current
Protective_relay
One of the Norwegian language standards
for gender, number and definiteness. In contrast, participles in Bokmål are only in general inflected for number and definiteness and shares many of the
Nynorsk
Study of vector bundles, principal bundles, and fibre bundles
this case Donaldson's theorem asserts that if the four-manifold has negative-definite intersection form (4-manifold), and if the principal bundle has structure
Gauge_theory_(mathematics)
Halakhic term for derogatory speech
tongue") is the halakhic term for speech about a person or persons that is negative or harmful to them, even if it is true. It is speech that damages the person(s)
Lashon_hara
Criterion for positivity of a Hermitian matrix
M_{n}} is strictly positive definite shows that all principal minors (not necessarily the leading principal minors) are non-negative. For the reverse implication
Sylvester's_criterion
Generalization of the normal-form game
diagonally-strictly-concave at r is that the symmetric matrix G(x,r)+GT(x,r) is negative definite. See the paper for an example for bimatrix games. Consider a dynamic
Concave_game
Number whose square is a given number
number or expression underneath the radical sign, in this case, 9. For non-negative x, the principal square root can also be written in exponent notation,
Square_root
Endangered Uralic language of Scandinavia
always marked identically, while the marking of the object depends on definiteness. The verb agrees with the subject in person and number. The TAM categories
Southern_Sámi
Way of describing the divine by explaining what God is not
Apophatic theology, also known as negative theology and the Via Negativa, is a form of theological thinking and religious practice which attempts to approach
Apophatic_theology
travel, tourism, insurance
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
Female
Native American
Native American Hopi name YOKI means "rain."
Female
Native American
Native American Sioux name WEEKO means "pretty."
Male
Native American
Native American Algonquin name ACHAK means "spirit."
Girl/Female
Indian, Sikh
Demolishing Negative Energy
Female
Native American
Native American Hopi name WAKI means "shelter."
Male
Native American
Native American Sioux name CHAYTON means "falcon."
Male
Native American
Native American Algonquin name CHOGAN means "blackbird."
Male
Native American
Native American Navajo name ASHKII means "boy."
Male
Native American
Native American Algonquin name ABUKCHEECH means "mouse."
Male
Native American
Native American Algonquin name ABOOKSIGUN means "wildcat."
Male
Native American
Native American Algonquin name CHANSOMPS means "locust."
Female
Native American
Native American Algonquin name WIKIMAK means "wife."
Female
Native American
Native American Sioux name WITASHNAH means "virginal."
Female
Native American
Native American Hopi name WUTI means "woman."
Male
Native American
Native American Hopi name CHOOVIO means "antelope."
Female
Native American
Native American Hopi name YAMKA means "blossom."
Female
Native American
Native American Hopi name ZIHNA means "spins."
Female
Native American
Native American Dakota name ZITKALA means "bird."
Male
Native American
Native American Algonquin name ASKOOK means "snake."
Female
Native American
Native American name APONI means "butterfly."
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
NEGATIVE DEFINITENESS
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