Parole in English per 'Any tensor whose value is based on an eigenfunction'
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verb
noun
- (engineering, computing) A multidimensional array with (at least) two dimensions.
- (anatomy) A muscle that tightens or stretches a part, or renders it tense.
- (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.
- any of several muscles that cause an attached structure to become tense or firm
- a generalization of the concept of a vector
adj
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
noun
- (linear algebra) A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
- (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
adj
- (mathematics, physics) Eigen-; designating a function or value which is an eigenfunction or eigenvalue.
- (algebraic geometry, of a morphism of schemes) Separated, of finite type, and universally closed.
- (usually postpositive) In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).
- (topology, of a function) Continuous, mapping closed sets to closed sets, and such that the preimage of every point is compact.
- (often postpositive) In the very strictest sense of the word.
- (mathematics) Being strictly part of some other thing (not necessarily explicitly mentioned, but of definitional importance), and not being the thing itself.
- Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.)
- Belonging to oneself or itself; own.
- Following the established standards of behavior or manners; correct or decorous.
- Suited or acceptable to the purpose or circumstances; fit, suitable.
- (heraldry) Portrayed in natural or usual coloration, as opposed to conventional tinctures.
- (of a city or town) Including only the core areas while excluding surrounding suburbs
- (algebraic geometry, of a variety over a field k) Such that unique morphism from the variety to k is proper (as above).
- (mathematical analysis, of a metric space) Such that every closed ball is compact.
- (set theory, of a class) Not being a set.
- (now regional) Attractive, elegant.
- (grammar) Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter.
- Pertaining exclusively to a specific thing or person; particular.
- (now colloquial) Utter, complete.
- (topology, of a function) Such that the preimage of every compact set is compact.
- appropriate for a condition or purpose or occasion or a person's character, needs
- limited to the thing specified
- marked by suitability or rightness or appropriateness
- having all the qualities typical of the thing specified
adv
noun
noun
- (mathematics) A metric tensor.
- Abbreviation of metric system.
- A measure for something; a means of deriving a quantitative measurement or approximation for otherwise qualitative phenomena (especially used in engineering).
- (mathematical analysis) A function which satisfies a particular set of formal conditions, created to generalize the notion of the distance between two points. Formally, a real-valued function d on M×M, where M is a set, is called a metric if (1) d(x,y)=0 if and only if x=y, (2) d(x,y)=d(y,x) for all pairs (x,y), and (3) d obeys the triangle inequality.
- a system of related measures that facilitates the quantification of some particular characteristic
- a function of a topological space that gives, for any two points in the space, a value equal to the distance between them
- a decimal unit of measurement of the metric system (based on meters and kilograms and seconds)
adj
verb
adj
- (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...
adj
- (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...
noun
- (linear algebra) A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
- (physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
adj
noun
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
noun
- (linear algebra) A scalar λ, such that there exists a non-zero vector x (a corresponding eigenvector) for which the image of x under a given linear transformation A is equal to the image of x under multiplication by λ; i.e. Ax=λx.
- (mathematics) any number such that a given square matrix minus that number times the identity matrix has a zero determinant
noun
- (mathematics) A metric tensor.
- Abbreviation of metric system.
- A measure for something; a means of deriving a quantitative measurement or approximation for otherwise qualitative phenomena (especially used in engineering).
- (mathematical analysis) A function which satisfies a particular set of formal conditions, created to generalize the notion of the distance between two points. Formally, a real-valued function d on M×M, where M is a set, is called a metric if (1) d(x,y)=0 if and only if x=y, (2) d(x,y)=d(y,x) for all pairs (x,y), and (3) d obeys the triangle inequality.
- a system of related measures that facilitates the quantification of some particular characteristic
- a function of a topological space that gives, for any two points in the space, a value equal to the distance between them
- a decimal unit of measurement of the metric system (based on meters and kilograms and seconds)
adj
verb
noun
- (linear algebra) A vector that is only scaled (not rotated out of its span) under a particular linear transformation; a left or right eigenvector depending on context; (more formally) given a linear transformation A, a vector x such that Ax=λx [or xA=λx] for some scalar λ (called the eigenvalue).
- (physics, engineering) A right eigenvector; given a matrix A, the eigenvector of the transformation "left-side multiplication by A."
noun
- (mathematics, linear algebra) The set of eigenvalues of a matrix.
- (psychology, education, usually with the) The autism spectrum.
- Specifically, a range of colours representing light (electromagnetic radiation) of contiguous frequencies; hence electromagnetic spectrum, visible spectrum, ultraviolet spectrum, etc.
- (mathematics, functional analysis) Of a bounded linear operator A, the set of scalar values λ such that the operator A—λI, where I denotes the identity operator, does not have a bounded inverse; intended as a generalisation of the linear algebra sense.
- A range; a continuous, infinite, one-dimensional set, possibly bounded by extremes.
- The image of something seen that persists after the eyes are closed.
- (chemistry) The pattern of absorption or emission of radiation produced by a substance when subjected to energy (radiation, heat, electricity, etc.).
- (commutative algebra, algebraic geometry) An abstract object in mathematics created from a commutative ring R and denoted operatorname Spec(R) or operatorname SpecR and said to be the spectrum of R; useful in the study of such rings for providing a geometric object which encodes many of the properties R, and in modern geometry for generalizing the notion of an algebraic variety to that of an affine scheme. Formally, the set of all prime ideals R equipped with the Zariski topology and augmented with a sheaf of rings called the structure sheaf, generated by the B-sheaf on the distinguished open sets D_f which assigns the localization of R at f to each set D_f, regarded as a ring of functions on D_f. See Spectrum of a ring on Wikipedia.Wikipedia
- an ordered array of the components of an emission or wave
- a broad range of related objects or values or qualities or ideas or activities
verb
noun
- (engineering, computing) A multidimensional array with (at least) two dimensions.
- (anatomy) A muscle that tightens or stretches a part, or renders it tense.
- (mathematics, linear algebra, physics) A mathematical object that describes linear relations on scalars, vectors, matrices and other algebraic objects, and is represented as a multidimensional array.
- any of several muscles that cause an attached structure to become tense or firm
- a generalization of the concept of a vector
adj
- (mathematics, of an eigenvalue) Having multiple different (linearly independent) eigenvectors.
- (physics) Having the same quantum energy level.
- Having lost functionality in general.
- (of an encoding or function) Having multiple domain elements correspond to one element of the range.
- (of qualities) Having deteriorated, degraded or fallen from normal, coherent, balanced and desirable to undesirable and typically abnormal.
- (mathematics) Qualitatively different, usually simpler, than typical objects of its class.
- (of a person or system) Having lost good or desirable qualities; hence also having bad character or habits, base, immoral, corrupt. ABR
- unrestrained by convention or morality
noun
verb
adj
- (mathematics, physics) Eigen-; designating a function or value which is an eigenfunction or eigenvalue.
- (algebraic geometry, of a morphism of schemes) Separated, of finite type, and universally closed.
- (usually postpositive) In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).
- (topology, of a function) Continuous, mapping closed sets to closed sets, and such that the preimage of every point is compact.
- (often postpositive) In the very strictest sense of the word.
- (mathematics) Being strictly part of some other thing (not necessarily explicitly mentioned, but of definitional importance), and not being the thing itself.
- Excellent, of high quality; such as the specific person or thing should ideally be. (Now often merged with later senses.)
- Belonging to oneself or itself; own.
- Following the established standards of behavior or manners; correct or decorous.
- Suited or acceptable to the purpose or circumstances; fit, suitable.
- (heraldry) Portrayed in natural or usual coloration, as opposed to conventional tinctures.
- (of a city or town) Including only the core areas while excluding surrounding suburbs
- (algebraic geometry, of a variety over a field k) Such that unique morphism from the variety to k is proper (as above).
- (mathematical analysis, of a metric space) Such that every closed ball is compact.
- (set theory, of a class) Not being a set.
- (now regional) Attractive, elegant.
- (grammar) Used to designate a particular person, place, or thing. Proper nouns are usually written with an initial capital letter.
- Pertaining exclusively to a specific thing or person; particular.
- (now colloquial) Utter, complete.
- (topology, of a function) Such that the preimage of every compact set is compact.
- appropriate for a condition or purpose or occasion or a person's character, needs
- limited to the thing specified
- marked by suitability or rightness or appropriateness
- having all the qualities typical of the thing specified
adv
noun
adj
- (mathematics) of a particular kind of eigenvalue problem involving a nonlinear function on the reals that is continuous, positive, and monotone.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...
adj
- (mathematics) an eigenvalue problem that would be a positone eigenvalue problem except that the nonlinear function is not positive when its argument is zero.
- for scriptstyle λ>0 under the assumption that scriptstyle f: ℝ→ ℝ is continuous, positive, monotone. For this reason such problems were named positone... If the nonlinearity scriptstyle f: ℝ→ ℝ is continuous, monotone and scriptstyle f(0)<0,...then the eigenvalue problem is called semipositone...