If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

If the master of scops who was most responsible for the poem ever used kennings that were traditional, he was at least partly deprived of free will and not inclined towards shrewd and sophisticated misuse of speech elements.

If elements in the sample space increase arithmetically, when placed in some order, then the median and arithmetic average are equal.

If so, they may have originally comprised residual Celtic elements in central eastern Europe such as the Cotini, who formed a Celtic enclave in the Germanic-speaking zone and are described by Tacitus as iron-ore miners working as tributaries of the powerful Quadi Germanic people.

More formally a k-combination of a set S is a subset of k distinct elements of S. If the set has n elements the number of k-combinations is equal to the binomial coefficient

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

If so, it is unclear how much Tatian may have borrowed from this previous author in determining his own narrative sequence of Gospel elements.

If ~ is an equivalence relation on X, and P ( x ) is a property of elements of X, such that whenever x ~ y, P ( x ) is true if P ( y ) is true, then the property P is said to be well-defined or a class invariant under the relation ~.

If is an equivalence relation on, and is a property of elements of such that whenever, is true if is true, then the property is said to be an invariant of, or well-defined under the relation.

If found, it removes it by concatenating all the elements prior to it with all the elements after it.

) If a set is finite, its elements may be written as a sequence:

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.

If the Gospel of Barnabas is seen as an attempted synthesis of elements from both Christianity and Islam, then 16th and 17th century parallels can be suggested in Morisco and anti-Trinitarian writings.

If so, these huge stars would have quickly consumed their supply of fuel and became supernovae, releasing heavy elements into the interstellar medium.

If a game has a board, the board is usually irregular rather than uniform or symmetric ( like Risk rather than chess or Scrabble ); the board is often random ( like Settlers of Catan ) or has random elements ( like Tikal ).

If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional ( grassman -) Jordan algebra, which has the symmetry group of one of the exceptional Lie groups ( F < sub > 4 </ sub >, E < sub > 6 </ sub >, E < sub > 7 </ sub > or E < sub > 8 </ sub >) depending on the details.

If a set of non-identical numbers is subjected to a mean-preserving spread — that is, two or more elements of the set are " spread apart " from each other while leaving the arithmetic mean unchanged — then the geometric mean always decreases.

If a set of non-identical numbers is subjected to a mean-preserving spread — that is, two or more elements of the set are " spread apart " from each other while leaving the arithmetic mean unchanged — then the harmonic mean always decreases.

If the domain is the real numbers, then each element in Y would correspond to two different elements in X (± x ), and therefore ƒ would not be invertible.

If R is the direct sum of the rings R < sub > 1 </ sub >,..., R < sub > n </ sub >, then the identity elements of the rings R < sub > i </ sub > are central idempotents in R, pairwise orthogonal, and their sum is 1.

If the figure comprises more than three elements, it is said to be rekit “ extended ”.

If a particular KR is inadequate in some way, that set of problematic KR elements may be transformed by importing them into a KBS, modified and operated on to eliminate the problematic elements or augmented with additional knowledge imported from other sources, and then exported into a different, more appropriate KR.

If some dances, such as polka, cross ethnic boundaries and even cross the boundary between " folk " and " ballroom dance ", ethnic differences are often considerable enough to mention, e. g., Czech polka vs. German polka.

If modern mathematical practices are what distinguish modern professional mathematicians from older ideas of folk mathematics.

" If You're Happy and You Know It " is a popular repetitive children's song, stemming from an old Latvian folk song.

The 2009 album Until the Earth Begins to Part by Scottish folk indie-rock band Broken Records features a song, " If Eilert Løvborg Wrote A Song, It Would Sound Like This ".

Roger Waters contributes a folk ballad called " If ", playing acoustic guitar.

Other musicians included John Fahey, one of the first " folk " musicians to gain national appeal, Peter Tork ( of The Monkees ), underground legend Tim Buckley, guitarist Link Wray, pop singer and songwriter Billy Stewart, country singer Patsy Cline, guitarist Danny Gatton, doo wop bands The Orioles ( based out of D. C., though from Baltimore ) and The Clovers, Scott McKenzie ( known for " If You're Going to San Francisco "), R & B singer Ruth Brown, and country star Roy Clark.

The new infusion of African and traditional British folk influences re-energized the band for two more albums: Shift ( 2001 ) and If Not Now ( 2003 ).

If at all, it was the other way round and many had folk narratives, traditions, myths and legends to bolster their sense of identity and cultural uniqueness.

Songs such as his modern-day rewrite of the traditional folk songs " King Jaja " and " See My Little Brown Girl " ( as " If You See My Girl ") and the instrumental " Tuk, Tabla, and Fedounoum " ( from his 2009 album Blood Mates ), are examples of making the old new and relatable to contemporary audiences.

If Amália is still the most recognizable Portuguese name in music, today the biggest exportations are bands like Moonspell ( metal ), Madredeus ( fado and folk inspired ), Buraka Som Sistema ( electro / kuduro / breakbeat ), Da Weasel, Sandro G ( hip hop ), Blasted Mechanism ( experimental electro-rock ) or Wraygunn ( rock, blues ), and artists like Mariza ( fado ).

If it is to be successful it must be folk planning.

If one extends the definition beyond the realm of pop, precursors can be found in musique concrète, as well as the classical practice of ( re -) arranging traditional folk material and the jazz tradition of reinterpreting standards.

" A themed LP entitled " Dominique " featured the singers with their musically talented siblings & cousins performing a variety of 1960s folk songs, including " Where Have All the Flowers Gone ," " If I Had My Way ( The Sermon of Samson )," as well as the title track.

* There is a common motif in Russian folk tales, where a vityaz ( Russian knight ) comes to a fork in the road and sees a menhir with an inscription that reads: " If you ride to the left, you will lose your horse, if you ride to the right, you will lose your head ".

Wan Li was immortalised in the folk saying " If you want to eat rice, look for Wan Li.

During the Vietnam War the first rock protest songs were heard, inspired by the songs of folk musicians such as Woody Guthrie and Bob Dylan, which ranged from abstract evocations of peace Peter, Paul and Mary's " If I Had a Hammer " to blunt anti-establishment diatribes Crosby, Stills, Nash & Young's " Ohio ".

If Hitler liked neoclassical art, that means that classicism in every form is Nazi ; if Hitler wanted to strengthen the German family, that makes the traditional family ( and its defenders ) Nazi ; if Hitler spoke of the " nation " or the " folk ," then any invocation of nationality, ethnicity, or even folkishness is Nazi ...

The book " If You're A Wee Bit Irish: a chart of old Irish families collected from folk tradition " by William Durning ( 1978 ) recounts an alleged ancestry of Caoilte back to Adam.

If traditional materials are inaccessible, new materials are often substituted, resulting in contemporary expressions of traditional folk art forms.

The song is an Irish folk style ballad, written by Jem Finer and Shane MacGowan, and featured on The Pogues ' album If I Should Fall from Grace with God.

The Beatles ' late 1965 album, Rubber Soul, contained a number of songs clearly influenced by the American folk rock boom, such as " Nowhere Man " and " If I Needed Someone ".

Highland Laddie, also known as Hielan ' Laddie, is the name of an ancient Scottish popular folk tune If thou ' lt play me fair play, but as with many old melodies, various sets of words can be sung to it and Robert Burns ' poem ' Highland Laddie, Highland Lassie ' has been the most memorable.

If thou ' lt play me fair play has been reworked several times since Burns set down his words and the latest has been a version recorded by the Newfoundland folk rock band Great Big Sea as " Donkey Riding.

I will correct it when I can ) and Angela Sperou were putting together a book called If Stones Could Speak which explored the history of Derry / Londonderry and the sad divisions that maintained a conflict which we now know had nothing to do with ordinary folk from both communities, but which was tragically foisted on us by the greed of a few elitist Irish morons and their British counterparts in England.