lojbo jufsisku
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fu'ivla x1 is an eigenvalue (or zero) of linear transformation/square matrix x2, associated with/'owning' all vectors in generalized eigenspace x3 (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspace-generalization' power/exponent x4 (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x5 For any eigenvector v in generalized eigenspace x3 of linear transformation x2 for eigenvalue x1, where I is the identity matrix/transformation that works/makes sense in the context, the following equation is satisfied: ((x2 - x1 I)^x4)v = 0. When the argument of x4 is 1, the generalized eigenspace x3 is simply a strict/simple/basic eigenspace; this is the typical (and probable cultural default) meaning of this word. x4 will typically be restricted to integer values k > 0. x2 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 "eigen-ness", the eigenvalue is given the primary terbri (x1). When filling x3 and/or x4, x2 and x1 (in that order of importance) should already be (at least contextually implicitly) specified. x3 is the set of all eigenvectors of linear transformation x2, endowed with all of the typical operations of the vector space at hand. The default includes the zero vector (else the x3 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 x3. In other words there may or may not be more than one linearly independent vector in the eigenspace x3 for a given eigenvalue x1 of linear transformation x2. x3 is the unique generalized eigenspace of x2 for given values of x1 and x4. x1 is not necessarily the unique eigenvalue of linear transformation x2, 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 x2 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 x1 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 x3 is specified by a set of vectors, the span of that set should fully yield the entire eigenspace of the linear transformation x2 associated with eigenvalue x1, 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 x5 of the eigenvalue does not entail degeneracy (of eigenspace) if greater than 1; it is the integer number of occurrences of a given eigenvalue x1 in the multiset of eigenvalues (spectrum) of the given linear transformation/square matrix x2. In other words, the characteristic polynomial can be factored into linear polynomial primes (with root x1) which are exponentiated to the power x5 (the multiplicity; notably, not x4). For x4 > x5, the eigenspace is trivial. x2 may not be diagonalizable. The scalar zero (0) is a naturally permissible argument of x1 (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 x3 is a type of klesi, with the property of being closed under linear transformation x2 (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
experimental gismu x1 is clockwise/right-turn-direction of[/to] x2 along/following track x3 [path] in frame of reference x4 (where the axis is within the region defined by the track as the boundary, as viewed from and defined by view(er) x4; see notes); x1 is locally to the right of x2, according to x4, constrained along x3; x1 is along a right turn from x2 along path x3, as viewed in frame x4. Angular/curling direction: clockwise. he orientation of the path determines x4 but does not factor into consideration for x3. Further glosses: clockwise, locally rightward, right-turning (with no bulk translation) in a way that would be characterized as "negative" by the right-hand rule (aligned with and in the direction of a basis vector, at least for a given component). x1 is left-handedly/clockwise(ly) oriented relative to x2 on/along x3 in frame of reference x4. x1 is left-handed (one sense) from x2 [more accurately: moving from x2 to x1 requires a(n imaginary) motion that is left-handed about/along x3 as seen in frame/orientation/perspective x4]. x1 is to the path-following right of x2 (where the path is connected; as such, x1 is also be to the path-following left of x2, although there is an implication that the former is the smaller (or equal-length) path). See also: zucna, du'ei (left-handed vectorial cross product), du'oi (modal). Proposed short rafsi: -tso-.
lujvo x1=g1 sexually violates/harms/rapes/violates the sexual rights of victim x2=g2=xai2=k2, violation by sexual activity (sex used as a weapon/means of harm), in property x3=xai3 (ka) by resulting in injury x4=xai4 (state), violating right x5=k1 (event) which is morally/legally guaranteed but actually violated under standards x6=k3. Violated right k1 (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 harmer-victim relationship enforced by this word (and, specifically, xai1 and xai2=k2). See also: glexai, xaigle, vilgle, glevlile, glevilxaigau, glekrali, glecu'akrali, glekralyxai, kralyxai.
fu'ivla x1 is a bus/coach for carrying passengers x2, propelled by x3 See also sorprekarce, sorpeka, trene, taksi. For denoting passengers, engine, towns and cities etc. used in combination with karce, carce, marce, tcadu.
fu'ivla x1 (agent) consigns (by thought, word, or deed) x2 (patient) to fate x3 (abstraction) So-called "neutral-dapma"; zandapma would be the connotationally positive form, while dapma would be the connotationally negative form. See pacna, dimna, a'o, di'ai
fu'ivla x1 is Avogadro constant N_{A} [ approximately equal to: 6.02214129(27)×10^{23} mol^{−1}], expressed in units x2 in paradigm/system/metaphysics/universe x3 (default: this, our actual, physical universe) See also plankexu, tcelerita, gravnutnoia, boltsemaku, ocnerta, molro, kamre
gismu rafsi: bac x1 exceeds/is beyond limit/boundary x2 from x3 in property/amount x4 (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.
gismu rafsi: ban bau x1 is a/the language/dialect used by x2 to express/communicate x3 (si'o/du'u, not quote). Also tongue. See also tance, cusku, ve tavla, valsi, gerna, jufra, natmi, slaka.
gismu rafsi: bra x1 is big/large in property/dimension(s) x2 (ka) as compared with standard/norm x3. See also banli, clani, ganra, condi, plana, cmalu, rotsu, banro, xanto.
experimental gismu x1 is an omnibus for carrying x2 in medium x3 propelled by x4. Cf. sorprekarce; pavloibasfa for single-decker, relyloibasfa for double-decker jonbasfa for articulated, clajonbasfa for bi-articulated, dizbasfa for low-floor, drucaubasfa for open top, kumbasfa for coach, dicybasfa for trolleybus.
lujvo n1=l1=b1 is the night after b2=l2 at location n3. cabycte is tonight, whether or not it is currently night yet. bavlamcte is tomorrow night, even if cabycte is still in the future. Cf. nicte, prulamcte, bavlamdei.
fu'ivla x1 is to the north of x2 according to frame of reference x3. Synonymous to berti. See be'a. Set: be'arna du'arna ne'urna vu'arna. This set is invented for those who prefer the sumtcita over the gismu, due to all starting with different letters.
experimental gismu x1 is the "beneficiary"/intended-recipient of x2 (event/action), as intended by x3 // x2 is done for x1 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
fu'ivla x1 pertains to the Laurasian supercontinent/large subcontinent in aspect x2, more specifically associated with time period or arrangement x3 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
gismu rafsi: bil x1 is military/regimented/is strongly organized/prepared by system x2 for purpose x3. 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.
lujvo v1 is an insurance premium for an insurance sold from v2=b1 to b2=v4, which is v3. v2=b1 and b2=v4 do not neccessarily need to be human, these could also refer to abstract entities, like companies. See also: binra, vecnu and ve.