Synonyms for monomial or Related words with monomial
Examples of "monomial"
An induced representation of a one dimensional representation is called a
representation, because it can be represented as
matrices. Some groups have the property that all of their irreducible representations are
, the so-called
In this section only finite groups are considered. A
group is solvable by , presented in textbook in and . Every supersolvable group and every solvable A-group is a
group. Factor groups of
, but subgroups need not be, since every finite solvable group can be embedded in a
group, as shown by and in textbook form in .
as a linear combination of monomials, where is a finite subset of and the are all nonzero. When a
order has been chosen, the leading
is the largest in , the leading coefficient is the corresponding , and the leading term is the corresponding . "Head"
/coefficient/term is sometimes used as a synonym of "leading". Some authors use "
" instead of "term" and "power product" instead of "
". In this article, a
is assumed to not include a coefficient.
matrices occur in representation theory in the context of
representation of a group "G" is a linear representation "ρ" : "G" → GL("n", "F") of "G" (here "F" is the defining field of the representation) such that the image "ρ"("G") is a subgroup of the group of
Furthermore, if formula_31 is the highest-degree
term in formula_20, then the highest-degree
term in formula_33 is formula_34. Consequently, the polynomial
In mathematics, a
is, roughly speaking, a polynomial which has only one term. Two definitions of a
may be encountered:
Although Gröbner basis theory does not depend on a particular choice of an admissible
orderings are specially important for the applications:
Let us consider a polynomial ring formula_32 in which the variables are split into two subsets "X" and "Y". Let us also choose an elimination
ordering "eliminating" "X", that is a
ordering for which two monomials are compared by comparing first the "X"-parts, and, in case of equality only, considering the "Y"-parts. This implies that a
containing an "X"-variable is greater than every
independent of "X".
symmetric polynomials of degree in , for instance
Since these conditions may be easier to verify for a
order defined through an explicit rule, than to directly prove it is a well-ordering, they are sometimes preferred in definitions of
Although the dimension and the degree do not depend on the choice of the
ordering, the Hilbert series and the polynomial formula_29 change when one changes of
This law of composition on formula_119 causes the "
triangularity property when expanded in the
The inverse of a non-negative matrix is usually not non-negative. The exception is the non-negative
matrices: a non-negative matrix has non-negative inverse if and only if it is a (non-negative)
matrix. Note that thus the inverse of a positive matrix is not positive or even non-negative, as positive matrices are not
, for dimension formula_2
is called the
representation of formula_1 in formula_119
similar to the "permutation representation" and the "
symmetric polynomials form a vector space basis: every symmetric polynomial "P" can be written as a linear combination of the
symmetric polynomials. To do this it suffices to separate the different types of
occurring in "P". In particular if "P" has integer coefficients, then so will the linear combination.
Since the word "
", as well as the word "polynomial", comes from the late Latin word "binomium" (binomial), by changing the prefix "bi" (two in Latin), a
should theoretically be called a "mononomial". "
" is a syncope by haplology of "mononomial".
In mathematics, in the area of algebra studying the character theory of finite groups, an M-group or
group is a finite group whose complex irreducible characters are all
, that is, induced from characters of degree 1 .
A useful property of the degree reverse lexicographical order is that a homogeneous polynomial is a multiple of the least indeterminate if and only if its leading
) is a multiple of this least indeterminate.
Copyright © 2017