aigne
fu'ivla x_{1} is an eigenvalue (or zero) of linear transformation/square matrix x_{2}, associated with/'owning' all vectors in generalized eigenspace x_{3} (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspacegeneralization' power/exponent x_{4} (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x_{5} For any eigenvector v in generalized eigenspace x_{3} of linear transformation x_{2} for eigenvalue x_{1}, where I is the identity matrix/transformation that works/makes sense in the context, the following equation is satisfied: ((x_{2}  x_{1} I)^x_{4})v = 0. When the argument of x_{4} is 1, the generalized eigenspace x_{3} is simply a strict/simple/basic eigenspace; this is the typical (and probable cultural default) meaning of this word. x_{4} will typically be restricted to integer values k > 0. x_{2} should always be specified (at least implicitly by context), for an eigenvalue does not mean much without the linear transformation being known. However, since one usually knows the said linear transformation, and since the basic underlying relationship of this word is "eigenness", the eigenvalue is given the primary terbri (x_{1}). When filling x_{3} and/or x_{4}, x_{2} and x_{1} (in that order of importance) should already be (at least contextually implicitly) specified. x_{3} is the set of all eigenvectors of linear transformation x_{2}, endowed with all of the typical operations of the vector space at hand. The default includes the zero vector (else the x_{3} eigenspace is not actually a vector space); normally in the context of mathematics, the zero vector is not considered to be an eigenvector, but by this definition it is included. Thus, a Lojban mathematician would consider the zero vector to be an (automatic) eigenvector of the given (in fact, any) linear transformation (particularly ones represented by a square matrix in a given basis). This is the logically most basic definition, but is contrary to typical mathematical culture. This word implies neither nondegeneracy nor degeneracy of eigenspace x_{3}. In other words there may or may not be more than one linearly independent vector in the eigenspace x_{3} for a given eigenvalue x_{1} of linear transformation x_{2}. x_{3} is the unique generalized eigenspace of x_{2} for given values of x_{1} and x_{4}. x_{1} is not necessarily the unique eigenvalue of linear transformation x_{2}, nor is its multiplicity necessarily 1 for the same. Beware when converting the terbri structure of this word. In fact, the set of all eigenvalues for a given linear transformation x_{2} will include scalar zero (0); therefore, any linear transformation with a nontrivial set of eigenvalues will have at least two eigenvalues that may fill in terbri x_{1} of this word. The 'eigenvalue' of zero for a proper/nice linear transformation will produce an 'eigenspace' that is equivalent to the entire vector space at hand. If x_{3} is specified by a set of vectors, the span of that set should fully yield the entire eigenspace of the linear transformation x_{2} associated with eigenvalue x_{1}, however the set may be redundant (linearly dependent); the zero vector is automatically included in any vector space. A multidimensional eigenspace (that is to say a vector space of eigenvectors with dimension strictly greater than 1) for fixed eigenvalue and linear transformation (and generalization exponent) is degenerate by definition. The algebraic multiplicity x_{5} of the eigenvalue does not entail degeneracy (of eigenspace) if greater than 1; it is the integer number of occurrences of a given eigenvalue x_{1} in the multiset of eigenvalues (spectrum) of the given linear transformation/square matrix x_{2}. In other words, the characteristic polynomial can be factored into linear polynomial primes (with root x_{1}) which are exponentiated to the power x_{5} (the multiplicity; notably, not x_{4}). For x_{4} > x_{5}, the eigenspace is trivial. x_{2} may not be diagonalizable. The scalar zero (0) is a naturally permissible argument of x_{1} (unlike some cultural mathematical definitions in English). Eigenspaces retain the operations and properties endowing the vectorspaces to which they belong (as subspaces). Thus, an eigenspace is more than a set of objects: it is a set of vectors such that that set is endowed with vectorspace operators and properties. Thus klesi alone is insufficient. But the set underlying eigenspace x_{3} is a type of klesi, with the property of being closed under linear transformation x_{2} (up to scalar multiplication). The vector space and basis being used are not specified by this word. Use this word as a seltau in constructions such as "eigenket", "eigenstate", etc. (In such cases, te aigne is recommended for the typical English usages of such terms. Use zei in lujvo formed by these constructs. The term "eigenvector" may be rendered as cmima be le te aigne). See also gei'ai, klesi, daigno


dutso
experimental gismu x_{1} is clockwise/rightturndirection of[/to] x_{2} along/following track x_{3} [path] in frame of reference x_{4} (where the axis is within the region defined by the track as the boundary, as viewed from and defined by view(er) x_{4}; see notes); x_{1} is locally to the right of x_{2}, according to x_{4}, constrained along x_{3}; x_{1} is along a right turn from x_{2} along path x_{3}, as viewed in frame x_{4}. Angular/curling direction: clockwise. he orientation of the path determines x4 but does not factor into consideration for x3. Further glosses: clockwise, locally rightward, rightturning (with no bulk translation) in a way that would be characterized as "negative" by the righthand rule (aligned with and in the direction of a basis vector, at least for a given component). x1 is lefthandedly/clockwise(ly) oriented relative to x2 on/along x3 in frame of reference x4. x1 is lefthanded (one sense) from x2 [more accurately: moving from x2 to x1 requires a(n imaginary) motion that is lefthanded about/along x3 as seen in frame/orientation/perspective x4]. x1 is to the pathfollowing right of x2 (where the path is connected; as such, x1 is also be to the pathfollowing left of x2, although there is an implication that the former is the smaller (or equallength) path). See also: zucna, du'ei (lefthanded vectorial cross product), du'oi (modal). Proposed short rafsi: tso.


kralyxaigle
lujvo x_{1}=g_{1} sexually violates/harms/rapes/violates the sexual rights of victim x_{2}=g_{2}=xai_{2}=k_{2}, violation by sexual activity (sex used as a weapon/means of harm), in property x_{3}=xai_{3} (ka) by resulting in injury x_{4}=xai_{4} (state), violating right x_{5}=k_{1} (event) which is morally/legally guaranteed but actually violated under standards x_{6}=k_{3}. Violated right k_{1} (event) may be implied by x4. The harm/violation must be by sexual activity (what one would consider gletu) and must be sexual in nature. Need not be violent. Harm may not be physical or even psychological/mental/emotional; it need only be a 'harm to one's rights' (in other words, a violation of loi krali). krali is an experimental gismu. The mutual symmetry of gle1 and gle2 is lost/broken by the harmervictim relationship enforced by this word (and, specifically, xai1 and xai2=k2). See also: glexai, xaigle, vilgle, glevlile, glevilxaigau, glekrali, glecu'akrali, glekralyxai, kralyxai.


aftobuso


apma


avgadro
fu'ivla x_{1} is Avogadro constant N_{A} [ approximately equal to: 6.02214129(27)×10^{23} mol^{−1}], expressed in units x_{2} in paradigm/system/metaphysics/universe x_{3} (default: this, our actual, physical universe) See also plankexu, tcelerita, gravnutnoia, boltsemaku, ocnerta, molro, kamre


bancu
gismu rafsi: bac x_{1} exceeds/is beyond limit/boundary x_{2} from x_{3} in property/amount x_{4} (ka/ni). On the other side of a bound, but not necessarily directly 'across' nor at the shortest plausible distance (per ragve); also not limited to position in space. See also dukse, ragve, zmadu, kuspe.


bangu


barda


basfa
experimental gismu x_{1} is an omnibus for carrying x_{2} in medium x_{3} propelled by x_{4}. Cf. sorprekarce; pavloibasfa for singledecker, relyloibasfa for doubledecker jonbasfa for articulated, clajonbasfa for biarticulated, dizbasfa for lowfloor, drucaubasfa for open top, kumbasfa for coach, dicybasfa for trolleybus.


bavlamcte


be'arna


benre
experimental gismu x_{1} is the "beneficiary"/intendedrecipient of x_{2} (event/action), as intended by x_{3} // x_{2} is done for x_{1} A "beneficiary" here is someone or something for which something is done, and this relation may be either beneficial or disadvantageous. Consider "I poisoned the cake for him" vs "I baked a cake for him" ("for him to eat" would be a purpose/goal). See also be'ei, kosmu, terzu'e, selxau


be'omronzdo
fu'ivla x_{1} pertains to the Laurasian supercontinent/large subcontinent in aspect x_{2}, more specifically associated with time period or arrangement x_{3} Not to be confused with Laurentia. x3 is a property of Laurasia itself (at the time in question, as determined by x1 and x2). This word could be used along the lines of other cultural gismu: x1 reflect Laurasian culture/lifestyle/"nationality" in aspect/nature x2. Confer: pangaio, gonduana, bemro, ropno, xazdo


bilni
gismu rafsi: bil x_{1} is military/regimented/is strongly organized/prepared by system x_{2} for purpose x_{3}. Also paramilitary; soldier in its broadest sense  not limited to those trained/organized as part of an army to defend a state (= bilpre). See also jenmi for a military force, sonci, ganzu, pulji.


binryvelve'u
