The Monster has a faithful 196, 883-dimensional representation in the 196, 884-dimensional Griess algebra, meaning that each element of the Monster can be expressed as a 196, 883 by 196, 883 matrix.

Now, the representation is faithful if is injective, that is, if the kernel of is trivial.

But every faithful G-set ( equivalently, every representation of G as a group of permutations ) determines a faithful functor G → Set.

Jordaens's Night Vision appears to be a very faithful representation of Phlegon's story and depicts the decisive moment or climax of the ancient tale.

In the narrow sense intended by Ruskin, only a faithful representation of experience, as it genuinely appears to the senses, escapes the pathetic fallacy.

Therefore, the reification data is always a faithful representation of the related reified aspect.

To be precise, the generalized permutation matrices are a ( faithful ) linear representation of this abstract wreath product: a realization of the abstract group as a subgroup of matrices.

According to another basic theorem, any group in the category of affine varieties has a faithful linear representation: we can consider it to be a matrix group over K, defined by polynomials over K and with matrix multiplication as the group operation.

Note that this means that algebraic group is narrower than Lie group, when working over the field of real numbers: there are examples such as the universal cover of the 2 × 2 special linear group that are Lie groups, but have no faithful linear representation.

It is a fairly faithful, if bowdlerized, representation, but notable for the addition of music and songs, including " Take it off the E string, play it on the G string " sung by Stanwyck.

If the homomorphism is in fact a monomorphism, the representation is said to be faithful.

In general it will not be a faithful representation.

associated to the spin structure via the spin representation where denotes the group of unitary operators acting on a Hilbert space It is worth noting that the spin representation is a faithful and unitary representation of the group.

Kushner made certain changes to his play ( especially Part II, " Perestroika ") in order for it to work on screen, but the HBO version is generally a faithful representation of Kushner's original work.

The first basic theorem of the subject is that any affine algebraic group is a linear algebraic group: that is, any affine variety V that has an algebraic group law has a faithful linear representation, over the same field.

For example the additive group of an n-dimensional vector space has a faithful representation as n + 1 × n + 1 matrices.

This is a Lie group that maps infinite-to-one to SL < sub > 2 </ sub >( R ), since the fundamental group is here infinite cyclic-and in fact the cover has no faithful matrix representation.

Nicholas of Cusa synthesized this strain of conciliarism, balancing hierarchy with consent and representation of the faithful.

Outside of Lie theory, the term fundamental representation is sometimes loosely used to refer to a smallest-dimensional faithful representation, though this is also often called the standard or defining representation ( a term referring more to the history, rather than having a well-defined mathematical meaning ).

And although Schnabel's pianism bristles with excitement, it is meticulously faithful to Schubert's dynamic markings and phrase indications.

Expressed differently: if the price for becoming a faithful follower of Jesus Christ is some form of self-destruction, whether of the body or of the mind -- sacrificium corporis, sacrificium intellectus -- then there is no alternative but that the price remain unpaid.

At common law allegiance is a true and faithful obedience of the subject due to his Sovereign.

The Roman Catholic celebration is associated with the doctrine that the souls of the faithful who at death have not been cleansed from the temporal punishment due to venial sins and from attachment to mortal sins cannot immediately attain the beatific vision in heaven, and that they may be helped to do so by prayer and by the sacrifice of the Mass.

The most meaningful apostolic succession for most Protestants, then, is a " faithful succession " of apostolic teaching.

Anointing is considered to be a public rather than a private sacrament, and so as many of the faithful who are able are encouraged to attend.

In some dioceses of the Russian Orthodox Church it is customary for the bishop to visit each parish or region of the diocese some time during Great Lent and give Anointing for the faithful, together with the local clergy.

According to the Bible, Amnon (, " faithful ") was the oldest son of David, King of Israel, with his wife, Ahinoam, who is described as " the Jezreelitess ".

It is derived from the washing of the bell with holy water by the bishop, before he anoints it with the oil of the infirm without and with chrism within ; a fuming censer is placed under it and the bishop prays that these sacramentals of the Church may, at the sound of the bell, put the demons to flight, protect from storms, and call the faithful to prayer.

The book is structured in two roughly equal parts, the story of the campaigns of the Israelites in central, southern and northern Canaan and the destruction of their enemies, followed by the division of the conquered land among the twelve tribes ; the two parts are framed by set-piece speeches by God and Joshua commanding the conquest and at the end warning of the need for faithful obedience of the Law ( torah ) revealed to Moses.

In Judges, Samuel and Kings Israel becomes faithless and God ultimately shows his anger by sending his people into exile, but in Joshua Israel is obedient, Joshua is faithful, and God fulfills his promise and gives them the land.

But the king they are given is Yahweh's gift, and Samuel explains that kingship can be a blessing rather than a curse if they remain faithful to their God.

He reminds them that God is just, exhorting them to be faithful as they await that justice.

From the time of the Protestant Reformation onward, it has been understood that there is no commonality between the Bible way, which is justification by faith in the shed blood of Jesus Christ, and salvation by works, which the faithful, practicing Catholic embraces.

The Ultimate end is a concept in the moral philosophy of Max Weber, in which individuals act in a faithful, rather than rational, manner.

That the assessment of the contemporary situation advanced by John Paul II is not binding on the faithful was confirmed by Cardinal Ratzinger when he wrote in 2004 that,

A bishop with jurisdiction — usually the bishop of the place where the candidate died or is buried, although another ordinary can be given this authority — gives permission to open an investigation into the virtues of the individual, responding to a petition by members of the faithful, either actually or pro forma.

The saint is assigned a feast day which may be celebrated anywhere within the Catholic Church, although it may or may not appear on the general calendar or local calendars as an obligatory feast, parish churches may be built in his or her honor, and the faithful may freely and without restriction celebrate and honor the saint.

Although a recognition of sainthood by the Pope does not directly concern a fact of divine revelation, it must still be " definitively held " by the faithful as infallible under ( at the very least ) the Universal Magisterium of the Church since it is a truth connected to revelation by historical necessity.

This is rather different to the modern version known in Wicca, though they have the same premise, that of the rules given by a great Mother Goddess to her faithful.

* In 1990, Gabrielle Beaumont created a film adaptation for a horror anthology television series Nightmare Classics titled " Carmilla ", which is one of the more faithful adaptations of the story, though the setting was transported to post-Civil War Deep South of the United States.

To Serenissimus such tribes as the Cossacks of the Don or those ex-bandits the Zaporogian Cossacks ( in whose islands along the lower Dnieper the Polish novelist Sienkiewicz would one day place With Fire And Sword ) were just elements for enforced resettlement in, say, Bessarabia, where, as `` the faithful of the Black Sea borders '', he could use their presence as bargaining points in the Czarina's territorial claims against Turkey.

And Paul Lipson, as Morris, the faithful one who never gets home to his Shirley's dinner, was fine, too.

Two conciliar letters were prepared, one to the clergy and faithful of Alexandria, the other to the bishops of Egypt and Libya, in which the will of the Council was made known.

As one Party faithful put it, " A savage man ... a bloody man.

With the advice of our brethren and of the entire Curia, as well as with the will and consent of the prefect, we decree the abolition of that evil custom which has hitherto prevailed among the porticani, namely, of disposing, contrary to the wish of the one deceased, of the property of porticani dying without heirs ; with this understanding, however, that in future the porticani remain faithful to the Roman Church, to us and to our successors.

Whoever manufactures or knowingly expends counterfeit money, shall be cut off from the communion of the faithful ( excommunicated ) as one accursed, as an oppressor of the poor and a disturber of the city.

He explained that Christ did not have this gift because his mission was to the Jews, " nor does each one of the faithful now speak save in one tongue "; for " no one speaks in the tongues of all nations, because the Church herself already speaks the languages of all nations ".

Thereafter, she and Joseph lived separate lives, though they never divorced and remained faithful to one another.

Whatever conflicts existed between the two men, Antony remained faithful to Caesar but it is worth mentioning that according to Plutarch ( paragraph 13 ) Trebonius, one of the conspirators, had ' sounded him unobtrusively and cautiously ... Antony had understood his drift ... but had given him no encouragement: at the same time he had not reported the conversation to Caesar '.

In 1412, Owain led one of the final successful raiding parties with his most faithful soldiers and cut through the King ’ s men, and consequently captured, and later ransomed, a leading Welsh supporter of King Henry's, Dafydd Gam (" Crooked David "), in an ambush in Brecon.

Through it all, Marge has remained faithful to Homer, despite temptations to the contrary such as the one in " Life on the Fast Lane " ( season one, 1990 ), where she resists the charming Frenchman Jacques and instead chooses to remain with Homer.

The church, of early 16th century style and plan, has three entrances, one for the faithful and the other two for monks and clergy.

Though they differ from one another in essence and not only in degree, the common priesthood of the faithful and the ministerial or hierarchical priesthood are nonetheless interrelated: each of them in its own special way is a participation in the one priesthood of Christ.

Bob Marley in France noted as a Rasta. By 1997, there were, according to one estimate, around one million Rastafari faithful worldwide.

* 22 ) Pastoral activity in the Catholic Church, Latin as well as Oriental, no longer aims at having the faithful of one Church pass over to the other ; that is to say, it no longer aims at proselytizing among the Orthodox.

It is believed by the faithful that on its way from the island the plague scratched one of the fortification stones of the old citadel to indicate its fury at being expelled ; St. Spyridon is also attributed the role of saving the island at the second great siege of Corfu of 1716.

He emphasized that no human creature can change this and therefore there exists only one road for the faithful, to the mother and from her to Christ and through Christ to the Father.