What does irreducible mean in math?
1 : impossible to transform into or restore to a desired or simpler condition an irreducible matrix specifically : incapable of being factored into polynomials of lower degree with coefficients in some given field (such as the rational numbers) or integral domain (such as the integers) an irreducible equation.
What is reducible and irreducible representation?
In a given representation (reducible or irreducible), the characters of all matrices belonging to symmetry operations in the same class are identical. The number of irreducible representations of a group is equal to the number of classes in the group.
What is meant by irreducible factor?
An irreducible factor is a factor which cannot be expressed further as a product of factors. Such a factorisation is called an irreducible factorisation.
How do you know if a function is reducible?
Use an argument by contradiction. If is reducible, it has a factor of degree 1 or a factor of degree 2. Use long division or other arguments to show that none of these is actually a factor. If a polynomial with degree 2 or higher is irreducible in , then it has no roots in .
What’s another word for irreducible?
In this page you can discover 22 synonyms, antonyms, idiomatic expressions, and related words for irreducible, like: unchangeable, imperishable, permanent, invariant, indestructible, isomorphism, reducible, irreducibility, incapable of being diminished, immutable and irrevocable.
What is reducible factor?
Irreducible quadratic factors are quadratic factors that when set equal to zero only have complex roots.
What do you mean reducible polynomial?
Definition of reducible polynomial : a polynomial expressible as the product of two or more polynomials of lower degree.
What does not uncongenial mean?
1 : not sympathetic or compatible uncongenial roommates. 2a : not fitted : unsuitable a soil uncongenial to most crops. b : not to one’s taste : disagreeable an uncongenial task.
What does Reducibility mean?
capable of being reduced
Medical Definition of reducible : capable of being reduced a reducible hernia.
What is reducible group?
Definition. Reducible representation of a group G. A representation of a group G is said to be “reducible” if it is equivalent to a representation Γ of G that has the form of Equation (4.8) for all T ∈ G. It follows from Equations (4.1) and (4.8) that. for n = 1, 2,…,s1 and all T ∈ G.
What’s another word for uncongenial?
In this page you can discover 30 synonyms, antonyms, idiomatic expressions, and related words for uncongenial, like: incongruous, asocial, discordant, discourteous, incompatible, inharmonious, uncivil, ungregarious, unpleasant, unsociable and incompatibility.
What is a Galvanism?
Definition of galvanism 1 : a direct current of electricity especially when produced by chemical action. 2 : the therapeutic use of direct electric current (as for pain relief) 3 : vital or forceful activity.
What does reducible mean in NP?
Reducibility for any problem (NP-hard or any other) means the possibility to convert problem A into other problem B. If we know the complexity of problem B then the complexity of problem A is at least the same as the complexity of problem A.
What does non reducible mean?
adjective. not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum. incapable of being brought into a different condition or form. Mathematics. of or relating to a polynomial that cannot be factored.
How do you use uncongenial in a sentence?
Those ideas were highly uncongenial at the time, largely neglected and resisted. There are no sheep-dogs trying to drive us into an uncongenial fold. It is uncongenial to raise this point in time of war, but it is of course a fact.
What are reducible and irreducible matrices?
In addition, a matrix is reducible if and only if its associated digraph is not strongly connected. A square matrix that is not reducible is said to be irreducible . Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1103, 2000.
When is a matrix reducible in MATLAB?
A matrix is reducible if and only if it can be placed into block upper-triangular form by simultaneous row/column permutations. In addition, a matrix is reducible if and only if its associated digraph is not strongly connected.
How do you know if a n × n is reducible?
We know A n × n is reducible, when there exists a permutation matrix P such that: P T A P = , where X and Z are both square.
How do you know if a matrix is irreducible?
If E is nonnegative and irreducible, and F is diagonal and positive (namely, all of its entries are positive), then EF is irreducible. Irreducibility of matrices can be easily tested using the associated directed graphs. A directed graph G n is a set of n vertices and a set of directed arcs joining two vertices.