seltau


lu sutra bajra li'u cu tanru zo sutra zo bajra
"melbi ractu" is a tanru (compound verb) with seltau "sutra" and tertau "bajra".


ziltau


tertau


ke'e'u
experimental cmavo Locks tanru modification order reversal (does not affect lujvo). {ke'e'unai} restores regular order Makes all tanru in the following text "selskiski"/"militarystyle": i.e. tertau come *before* seltau. This essentially puts ke'oi before every tanru. // This is an experimental cmavo in the truest sense of the word, used to test out "what if" Lojban chose "nounadjective" order, which does have several advantages (chief of them being that the selbriunit that describes the subject is uttered first), despite being unusual for English speakers.


ke'oi
experimental cmavo reverses modification order of contained tanru (does not affect lujvo). Marks a "selskiski"/"militarystyle"/"nounadjective" tanru, i.e. tertau come *before* seltau. This differs from co in that it does not affect the place structure of the sumti to the right; i.e. in {mi ke'oi broda brode do} (= {mi brode broda do}), both mi and do are arguments of broda. Default grouping is still left: {lo ke'oi ckule nixli cmalu melbi} resolves to {lo ke'oi (((ckule nixli) cmalu) melbi)}, which is equivalent to {lo melbi ke cmalu ke nixli ckule}. co does not (re)reverse the order of tanrumodification; it only changes place structure. See ke'e'u.


zi'oi
experimental cmavo fills and deletes (in the manner as {zi'o}) all terbri of immediately previous word that are not explicitly filled with a sumti Implicit/omitted zo'e will be deleted. Deletion is only meaningful if the immediately previous word is a brivla with at least one unfilled (explicitly) terbri. In a tanru or other complicated construct, only the most recent word undergoes this terbri deletion (not every term in the construct). A selbri converted to a sumti by gadri has x1 terbri filled for the purposes of this word; likewise is the case for terbri accessed by be or bei; seltau in the main level of a sumti are filled by the gadri as well for the purposes of this word.


dau'a
experimental cmavo gafyzmico: Reset all default specifications of immediately previous word to official definition specifications hereinafter (permanently) Restores all default specifications in the (terbri) structure of immediately previously uttered word so that implicit/omitted zo'e and di'au that may fill the terbri of that word are predefined/specific in reference and do indeed necessarily agree with the default setting explicitly specified in the discourseexternal/“official” definition of the word. The terbri are not filled by this word. Usage is only meaningful for a brivla with at least one terbri (regardless of being explicitly filled or otherwise). In a tanru or other complicated construct, only the most recent word undergoes this terbri default restoration (not every term in the construct). A selbri converted to a sumti by gadri has the x1 terbri filled for the purposes of this word, but the default setting of that terbri is so restored all the same; likewise is the case for terbri accessed by be or bei; seltau in the main level of a sumti are filled by the gadri as well for the purposes of this word. Affects all future uses of the word (permanent), until the end of the text/conversation or explicitly undone in some manner. See also: doi'a, de'au, zmico.


de'au
experimental cmavo gafyzmico: Cancellation (permanent) of all defaults in immediately previous word Cancels/overrides/ignores/"kills" all defaults (default specifications) in the (terbri) structure of immediately previously uttered word so that implicit/omitted zo'e and di'au that may fill the terbri of that word are general in potential reference (modulo context) and do not necessarily agree with the default setting explicitly specified in the discourseexterior/“official” definition of the word. The terbri are not filled by this word. Usage is only meaningful for a brivla with at least one terbri (regardless of being explicitly filled or otherwise). In a tanru or other complicated construct, only the most recent word undergoes this terbri default override (not every term in the construct). A selbri converted to a sumti by gadri has the x1 terbri filled for the purposes of this word, but the default setting of that terbri is so overridden all the same; likewise is the case for terbri accessed by be or bei; seltau in the main level of a sumti are filled by the gadri as well for the purposes of this word. Affects all future uses of the word (permanent), until the end of the text/conversation or explicitly undone in some manner. See also: dau'a, de'oi, zmico.


de'oi
experimental cmavo Cancellation (instant/usagewise; temporary) of all defaults in immediately previous word Cancels/overrides/ignores/"kills" all defaults (default specifications) in the (terbri) structure of immediately previously uttered word so that implicit/omitted zo'e and{di’au} that may fill the terbri of that word are general in potential reference (modulo context) and do not necessarily agree with the default setting explicitly specified in the discourseexternal/“official” definition of the word. The terbri are not filled by this word. Usage is only meaningful for a brivla with at least one terbri (regardless of being explicitly filled or otherwise). In a tanru or other complicated construct, only the most recent word undergoes this terbri default override (not every term in the construct). A selbri converted to a sumti by gadri has the x1 terbri filled for the purposes of this word, but the default setting of that terbri is so overridden all the same; likewise is the case for terbri accessed by be or bei; seltau in the main level of a sumti are filled by the gadri as well for the purposes of this word. The cancellation is only effective for the single occurrence/instant/usage of this word (the next use of the affected word will be implicitly accompanied by its terbri defaults, as defined elsewhere (by official definition or by other (permanent) modifications made to the word)). See also: doi'a, de'au, zmico.


doi'a
experimental cmavo gafyzmico: Reset all default specification of the immediately previous word to their respective discourseexternal/official definition specifications for this instance/usage only. Resets all defaults (default specifications) in the (terbri) structure of immediately previously uttered word so that implicit/omitted zo'e and di'au that may fill the terbri of that word are predefined/specific in reference and do indeed necessarily agree with the default setting explicitly specified in the discourseexterior/”official” definition of the word. The terbri are not filled by this word. Usage is only meaningful for a brivla with at least one terbri (regardless of being explicitly filled or otherwise). In a tanru or other complicated construct, only the most recent word undergoes this terbri default restoration (not every term in the construct). A selbri converted to a sumti by gadri has the x1 terbri filled for the purposes of this word, but the default setting of that terbri is so restored all the same; likewise is the case for terbri accessed by be or bei; seltau in the main level of a sumti are filled by the gadri as well for the purposes of this word. The restoration is only effective for the single occurrence/instant/usage of this word (the next use of the affected word will be implicitly accompanied by its terbri defaults, as defined elsewhere (by official definition or by other (permanent) modifications made to the word)). See also: dau'a, de'oi, zmico


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
