One may show in a straightforward manner that no possible vector can be an eigenvector of both matrices.

Tolkien's prose is unpretentious and straightforward, taking as given the existence of his imaginary world and describing its details in a matter-of-fact way, while often introducing the new and fantastic in an almost casual manner.

Most importantly, he began to build support among media elites, who appreciated his articulateness, straightforward manner, moderate positions, and his refusal to walk down the conservative path that all of the other Republicans were traveling.

However, results of group theory that talk about individual elements, or the order of specific elements or subgroups, normally cannot be generalized to group objects in a straightforward manner.

Many concepts from ring theory, such as ideals, Jacobson radicals, and factor rings can be generalized in a straightforward manner to this setting.

" This is the only film where Fields doesn't ad lib, and he plays the character in a straightforward manner ( although he did want to add a juggling sequence, and when this was denied, an anecdote about snakes, which was also denied ).

Her refreshingly straightforward manner and talk made her a powerful public speaker.

Unlike many parodies that are done in a straightforward manner for effect, French and Saunders uses the viewer's awareness of what is going on to further stretch out the joke.

( In the ensuing general elections, the NDA secured a majority and Vajpayee was reappointed Prime minister ( 11 October 1999 ) in a straightforward manner.

The story explains these magical elements as real occurrences, presented in a straightforward manner that places the " real " and the " fantastic " in the same stream of thought.

Sidney wrote an early version ( The Old Arcadia ) during a stay at Mary Herbert's house ; this version is narrated in a straightforward, sequential manner.

Themes of sex, drugs, and rock ' n ' roll appear, but never in a straightforward manner, neither encouraging nor discouraging, and many ( if not all ) of their songs are tinged with an ironic edge.

But Abel's mechanical problem requires the converse — given, we wish to find, from which an equation for the curve would follow in a straightforward manner.

Film Noir notes, " By developing the plot from the point-of-view of a neurotic and skillfully using flashback and fantasy scenes in a straightforward manner, the distinction between reality and Louise's imagination is blurred.

During that period, the newscast had evolved into a well-crafted package delivered in a straightforward manner, much like Cronkite's evening newscast.

This definition generalizes in a straightforward manner to a discrete signal with an infinite number of values such as a signal sampled at discrete times:

The definition of the power spectral density generalizes in a straightforward manner to finite time-series with such as a signal sampled at discrete times for a total measurement period.

Clark's films often deal with seemingly lurid material but are told in a straightforward manner.

At his confirmation hearings in the European Parliament MEPs described him as “ fluent and relaxed ” giving straightforward answers in a refreshing and engaging manner.

The Standard Model of particle physics contains only renormalizable operators, but the interactions of general relativity become nonrenormalizable operators if one attempts to construct a field theory of quantum gravity in the most straightforward manner, suggesting that perturbation theory is useless in application to quantum gravity.

The expansion Silent Threat continues the story in a straightforward manner.

Mode 13h provides programmers with a straightforward manner of access ( nicknamed chunky graphics ) to video memory at the expense of not being able to use some useful features that the VGA hardware was otherwise capable of providing.

In fact, it can be proved that this secondary LQR problem can be solved in a very straightforward manner.

The construction generalizes in straightforward manner to the tensor algebra of any module M over a commutative ring.

In the US this box is usually only attainable if the other letterboxer knows the password or passphrase which is sometimes cryptic, straightforward, almost non-existent, or silly.

Conversely, Plant sometimes used more straightforward blues-based lyrics dealing primarily with sexual innuendo, as in " The Lemon Song ", " Trampled Under Foot ", and " Black Dog ".

Although the requirement was straightforward in canon law, complications sometimes arose in a marriage between a Catholic and a non-Catholic, when one of the parties to the marriage did not have a home parish in the Roman Catholic Church.

The two musicians liked and respected one another, despite the difference in their approach to music-making: Monteux was scrupulous in his adherence to a composer's score and straightforward in his performances, while Mengelberg was well known for his virtuoso, sometimes wilful, interpretations and his cavalier attitude to the score (" Ve vill make some changements ", as an English player quoted him ).

The term cookbook is sometimes used metaphorically to refer to any book containing a straightforward set of already tried and tested " recipes " or instructions for a specific field or activity, presented in detail so that the users who are not necessarily expert in the field can produce workable results.

Conant was one of the first to realise that while this relationship was sometimes straightforward and simple, at other times it could be quite complex.

Wharton was accused in his Times obituary of " sometimes veer into the area of straightforward racism " and of being " prone to anti-semitic innuendo " for such passages as this:

For multiplication, the most straightforward algorithms used for multiplying numbers by hand ( as taught in primary school ) require O ( N < sup > 2 </ sup >) operations, but multiplication algorithms that achieve O ( N log ( N ) log ( log ( N ))) complexity have been devised, such as the Schönhage – Strassen algorithm, based on fast Fourier transforms, and there are also algorithms with slightly worse complexity but with sometimes superior real-world performance for smaller N. The Karatsuba multiplication is such an algorithm.

Motives for making them include allowing more debate, delaying the enactment of the legislation, or just sometimes a straightforward attempt to make the initiator of the legislation give up.

Sterile vivariums, sometimes used to ensure high levels of hygiene ( especially during quarantine periods ), generally have very straightforward, easily removable substrates such as paper tissue, wood chips and even newspaper.

Less gruff than his wife, Jerry Sheindlin displayed more humor and was straightforward, often registering mock indignation whenever litigants referred to him ( as they sometimes did ) as " Judge Judy's husband.

He displayed more humor and was straightforward, often registering mock indignation whenever litigants referred to him ( as they sometimes did ) as " Judge Judy's husband.

Performative writing is sometimes referred to by the alternative name of ' creative critical writing ' - which is not to be confused with straightforward creative writing.

As a commentator Miller became known for his straightforward and sometimes blunt remarks, which sometimes earned him the enmity of players.

When the visual representation is not straightforward but as complex as a rebus, this is sometimes called a rebus coat of arms.

In terms of style it often uses straightforward rock and roll, sometimes with elements of Americana and country.

While some captures featured in the show were easy and straightforward due to obvious oversights or mistakes by the offenders, many others were much tougher and sometimes required greater resources.

It is normally restricted to young, pre-pubescent children, and aside from its straightforward purpose of fun can sometimes also serve the purpose of allowing children to explore adult roles and relationships.

" Davis then answers the questions with basic facts delivered in short easy-to-read essays which have a straightforward approach, but sometimes grab the reader's attention by beginning with light humor and anachronistic comparisons, for example: " Even the astronauts who flew to the moon had a pretty good idea of what to expect ; Columbus was sailing, as Star Trek puts it, ' where no man has gone before '.

Unlike the more straightforward black metal of their contemporaries, Ulver began their career by incorporating elements of Norwegian folk music, sometimes using acoustic guitars, melody-focused songwriting and clean vocals.

Verses 42 100 are more straightforward ; they describe the physical beauty of the Goddess and are sometimes referred to as the Soundarya Lahari itself.