ciste
gismu rafsi: ci'e x_{1} (mass) is a system interrelated by structure x_{2} among components x_{3} (set) displaying x_{4} (ka). x_{1} (or x_{3}) is synergistic in x_{4}; also network; x_{2} also relations, rules; x_{3} also elements (set completely specified); x_{4} systemic functions/properties. See also cmavo list ci'e, cmima, girzu, gunma, stura, tadji, munje, farvi, ganzu, judri, julne, klesi, morna, tcana.


cmima
gismu rafsi: mim cmi x_{1} is a member/element of set x_{2}; x_{1} belongs to group x_{2}; x_{1} is amid/among/amongst group x_{2}. x_{1} may be a complete or incomplete list of members; x_{2} is normally marked by la'i/le'i/lo'i, defining the set in terms of its common property(ies), though it may be a complete enumeration of the membership. See also ciste, porsi, jbini, girzu, gunma, klesi, cmavo list mei, kampu, lanzu, liste.


girzu
gismu rafsi: gir gri x_{1} is group/cluster/team showing common property (ka) x_{2} due to set x_{3} linked by relations x_{4}. Also collection, team, comprised of, comprising; members x_{3} (a specification of the complete membership) comprise group x_{1}; cluster (= kangri). See also bende, ciste, cmima, gunma, panra, cabra, cecmu, kansa, klesi, lanzu, liste, vrici.


jutsi
gismu rafsi: jut x_{1} is a species of genus x_{2}, family x_{3}, etc.; [openended treestructure categorization]. Also subspecies, order, phylum; (places do not correspond to specific levels in the hierarchy; rather, x_{1} is at a "lower" or "bushier" part of the tree than x_{2}, x_{2} is "lower" than x_{3}, etc.; skipping a place thus means that there is one or more knownandunspecified levels of hierarchy between the two); not limited to Linnean animal/plant taxonomy. See also klesi, lanzu.


praperi
fu'ivla x_{1} is a strict/proper subx_{2} [structure] in/of x_{3}; x_{2} is a structure and x_{1} and x_{3} are both examples of that structure x_{2} such that x_{1} is entirely contained within x_{3} (where containment is defined according to the standard/characteristics/definition of x_{2}; but in any case, no member/part/element that belongs to x_{1} does not also belong to x_{3}) but there is some member/part/element of x_{3} that does not belong to x_{1} in the same way. If x2 is a (sub)set, then x1 is a proper subset of x3; if x2 is a mathematical/algebraic (sub)group, then x1 is a proper subgroup of x3; etc. Can also be used for describing proper sublakes (such as Lake Michigan), proper superselma'o, and other nonmathmetical usages. x3 is a proper superx2 of/with x1. Biological taxa, if comparable, are usually/hypothetically proper. See also: klesi, cmeta.


terpanryziltolju'i
lujvo x1=j2=p3 (ka; jo'u/fa'u term) is the minor difference in/between x2=p2 and x3=p1 that is to be ignored, their similarity being by standard/in geometry x4; x2 is the same as/similar to/parallels x3 in standard/geometry x4 up to/modulo/except for/ignoring unimportant difference x1; x1 is not the focus of the main consideration concerning the similarity between x2 and x3; x2 belongs to/is an element of the same equivalence class as x3, which depends on x4 in some way and which ignores the property x1. For example, tetrominoes "L" and "7" are similar up to the unimportant property of 90degree rotation; thus: loka carna keiku ly terpanryziltolju'i zebu loka mapti. x2 and x3 are symmetric; while with panra, x1 (which is x3 in terpanryziltolju'i) is possibly of importance/focus/attention, for terpanryziltolju'i, x2 is. Additionally, lo panra and lo se panra are identical, therefore conversion under te does not affect the x2 and x3 positions of panra, so the overall structure does not need to have undergone an additional conversion. See: panra, klesi, panrykle, panryzilbri


rakle
experimental gismu x_{1} is an atomic element in group x_{2} [usually, vertical column; denotes electron configuration and, thereby, chemical similarity with vertical neighbors] and period x_{3} [usually, horizontal row; denotes similarity in size with horizontal neighbors, as well as having the same number and type of electron shells as them] and belonging to other 'class'/'category'/'type'/having other properties x_{4} according to scheme/organization pattern/standard/periodic table x_{5}. x4 can be any category of similar elements, such as (but not limited to): metals, conductors, gases (at STP), or those elements which obey some sort of pattern following certain atomic/physical/chemical characteristics (such as first iönization energy, stability of nucleus, abnormalities in electron configuration according to naïve expectations, etc.). Groups may (presently) be hard to name (or unsystematic in such) since the periodic table may be infinitely large such that it is equipped with an infinite number of groups between any two mutually nonidentical groups. For now, use cmevla or brivla for designating groups; optionally, pick a representative member of that group. Periods can be designated similarly or by number (counting by ones from one (being the period containing hydrogen)). See also: ratykle, ratniklesi for nongismu options; ratni, klesi, navni, kliru, cidro, tabno, kijno, gapci, xukmi


ratniklesi
fu'ivla x_{1} is an atomic element in group x_{2} [usually, vertical column; denotes electron configuration and, thereby, chemical similarity with vertical neighbors] and period x_{3} [usually, horizontal row; denotes similarity in size with horizontal neighbors, as well as having the same number and type of electron shells as them] and belonging to other 'class'/'category'/'type'/having other properties x_{4} according to scheme/organization pattern/standard/periodic table x_{5}. Nongismu version of rakle. x4 can be any category of similar elements, such as (but not limited to): metals, conductors, gases (at STP), or those elements which obey some sort of pattern following certain atomic/physical/chemical characteristics (such as first iönization energy, stability of nucleus, abnormalities in electron configuration according to naïve expectations, etc.). Groups may (presently) be hard to name (or unsystematic in such) since the periodic table may be infinitely large such that it is equipped with an infinite number of groups between any two mutually nonidentical groups. For now, use cmevla or brivla for designating groups; optionally, pick a representative member of that group. Periods can be designated similarly or by number (counting by ones from one (being the period containing hydrogen)). See also: rakle, ratykle; ratni, klesi, navni, kliru, cidro, tabno, kijno, gapci, xukmi


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


kei'au
experimental cmavo mekso operator: finite result set derived from/on set A with/due to operator/function B under ordering of application C Equivalent to: lo'i li zy du ca'e li pe'o se'au mau'au B zai'ai vei ma'o xy boi ny ve'o boi tau sy boi C ku poi ke'a cmaci xanri zi'e poi ke'a mleca li ci'i zo'u tau sy klesi A. Acts on an operator/function (b) and produces all finite results of that operator being used on any allowable number of elements of the set A without repetition within any given application. The result must be defined (and finite, obviously). Application of the operator on nothing (the elements of the empty set) is generically allowed and follows convention (for example, an empty sum may evaluate to 0). Differs from kei'ai. Use mau'au and zai'ai for quoting B. C will be specified explicitly (possibly elsewhere) and/or via zoi'ai.
