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Like and definitions
Like the " dimension of image " characterization this can be generalized to a definition of the rank of a linear map: the rank of a linear map f from V → W is the minimal dimension k of an intermediate space X such that f can be written as the composition of a map V → X and a map X → W. While this definition does not suggest an efficient manner to compute the rank ( for which it is better to use one of the alternative definitions ), it does allow to easily understand many of the properties of the rank, for instance that the rank of the transpose of A is the same as that of A.
Like for the DFT, the normalization factor in front of these transform definitions is merely a convention and differs between treatments.
Like other definitions of theories, including Popper's, Kitcher makes it clear that a theory must include statements that have observational consequences.
Like extraordinary definitions, the ordinary magisterium may propose teachings both de fide credenda and de fide tenenda, and the latter may advance to the status of the former, and both are held to be infallible.
Like cassoulet or fondue, this French dish has its many regional definitions.

Like and is
Like most major works of synthesis, The History Of England is informed by the positive views of a first-class mind, and this is surely a major work.
Like ours, the economy of the space merchants must constantly expand in order to survive, and, like ours, it is based on the principle of `` ever increasing everybody's work and profits in the circle of consumption ''.
Like everything else in Rome, ruins and monuments alike, that house is lived in.
Like the recent Scheherazade from London ( High Fidelity, Sept. 1961 ), it is successful because emphasis has been placed on good musical and engineering practices rather than on creating sensational effects.
Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.
Like about half of the 1860 - 70 poems, it is a sonnet on a conventional theme -- the unhappiness of love.
Like Philadelphia's late Dr. Albert C. Barnes who kept his own great collection closed to the general public ( Time, Jan. 2 ), Thompson, at 61, is something of a legend in his own lifetime.
Like Mr. Loesser, Jerry Herman is both composer and lyriist for Milk And Honey ( R. C. A. Victor LOC 1065 ; ;
Like an alphabet the phonemes of syllable initials are represented by individual symbols, but like a syllabary the phonemes of the syllable finals are not ; rather, each possible final ( excluding the medial glide ) is represented by its own symbol.
Like his creation the Necronomicon, Alhazred is often referenced in works that are not generally considered part of the Cthulhu Mythos, either as a subtle nod to Lovecraft or to create a connection to his world.
Like Agatha Christie, she isn't overly fond of the detective she is most famous for creating – in Ariadne's case the Finnish sleuth Sven Hjerson.
Like Jehovah's Witnesses, Adventists use key phrases from the Bible, such as " For the living know that they shall die: but the dead know not any thing, neither have they any more a reward ; for the memory of them is forgotten " ( Eccl.
Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg's catalogue is estimated to have been precise to within approximately 20 minutes of arc.
Like an abbot, after being confirmed in her office by the Holy See, an abbess is solemnly admitted to her office by a formal blessing, conferred by the bishop in whose territory the monastery is located, or by an abbot or another bishop with appropriate permission.
Like all traits, there is variability in the intensity of fears of spiders, and those with more intense fears are classified as phobic.
Like most of the other Greek leaders, Ajax is alive and well as the Iliad comes to a close.
Like Achilles, he is represented ( although not by Homer ) as living after his death in the island of Leuke at the mouth of the Danube.
Like most dialects of English it is distinguished primarily by its vowel phonology.
Like the previous plan by Sensi, this new stadium is to be modeled after English stadiums.
Like in Hinduism, the aim is to prevent the accumulation of harmful karma.
Like the other atypical antipsychotics, it is believed to have antagonist activity at dopamine and serotonin receptors in the brain.
(" I'm Like the Bluebird ") All the money is in the hands of Cora Hoover Hooper, the stylish, ruthless mayoress and her cronies-Comptroller Schub, Treasurer Cooley, and Police Chief Magruder.
Like the F-5, the A-1 is under a MLU ( Mid Life Upgrade ) program as well, this upgrade giving a high commonality between the avionics of the A-1M ( MLU aircraft designation ), the F-5M and the newly introduced Embraer A / T-29.

Like and valid
Like monogamy, the term is often used in a de facto sense, applying regardless of whether the relationships are recognized by the state ( see marriage for a discussion on the extent to which states can and do recognize potentially and actually polygamous forms as valid ).
Like previous taxes, the stamp tax had to be paid in valid British currency, not in colonial paper money.
Like all XML schema languages, XSD can be used to express a set of rules to which an XML document must conform in order to be considered ' valid ' according to that schema.
Like the Prandtl-Glauert Rule, this is only valid for 2D flows, and only until transonic flow starts to appear.
)</ ref > Like the Law of Excluded Middle, this principle when extended to an infinite collection of individuals is disallowed by Intuitionistic logic .< ref > The < sup > o </ sup > of Kleene's formula * 49 < sup > o </ sup > indicates " the demonstration is not valid for both systems system and intuitionistic system ", Kleene 1952: 101 .</ ref > In classical logic, this principle is considered to be a law of thought.
Like the FCRs, PATs always occur in pairs, with the currently valid copy indicated by having a higher usage count.
Like any other financial instrument, trading consists of matching buyers and sellers between members of the exchange and then settling by depositing a valid allowance in exchange for the agreed financial consideration.

Like and criticism
Like the vision of Banquo's lineage, the banquet scene has also been the subject of criticism.
* Men Like Gods ( 1923 ) by H. G. Wells, men and women in an alternative universe live without world government in a perfected state of anarchy ; " Our education is our government ," a Utopian named Lion says ; sectarian religion, like politics, has died away, and advanced scientific research flourishes ; life is governed by " the Five Principles of Liberty ," which are privacy, free movement, unlimited knowledge, truthfulness, and free discussion and criticism.
" Like Shakespeare, her work has been the subject of reams of criticism and many books.
Like all forms of literary criticism, psychoanalytic criticism can yield useful clues to the sometime baffling symbols, actions, and settings in a literary work ; however, like all forms of literary criticism, it has its limits.
" Like a Prayer " courted heavy criticism due to its religious, sexual, and racially-oriented imagery.
Like other Asharites who believed that faith or taqlid should only apply to Islam and not to any ancient Hellenistic authorities, Ibn al-Haytham's view that taqlid should only apply to prophets of Islam and not to any other authorities formed the basis for much of his scientific skepticism and criticism against Ptolemy and other ancient authorities in his Doubts Concerning Ptolemy and Book of Optics.
The lyrics of the I Like Trains song " The Beeching Report " are a criticism of Dr Beeching and the Beeching Axe.
Like all Canadian banks, they endured criticism of its credit policies and resisted the introduction of a central bank to control the money supply and advise on fiscal policy.
Like its predecessor, however, the game was subject to criticism concerning the game's camera system.
Like Popper, MacIntyre attacked critical theorists like Adorno and especially Marcuse as obscurantists pontificating dogma in the authoritarian fashion of German professors of philosophy of their era — before World War II —( page 11 ); Popper made a similar criticism of critical theory's rhetoric, which reflected the culture of Hegelian social studies in German universities ( pp. 293 – 94 ).
Like its predecessor, Carmageddon II was subject to criticism for the level of violence portrayed in the game.
Speak gained critical acclaim for its portrayal of the trauma caused by rape .< ref name =" literature criticism online "> Barbara Tannert-Smith, author of " Like Falling Up Into a Storybook: Trauma and Intertextual Repetition in Laurie Halse Anderson's Speak.
Like other sequels in the Mega Man series, Mega Man 5 has suffered criticism for its lack of innovative gameplay and storytelling.
However Pepsi had no control over Madonna's own " Like A Prayer " music video, which debuted exclusively on MTV soon after — it generated heated criticism due to its provocative use of religious imagery and was condemned by the Vatican.
Like the book, the documentary attracted more support and criticism.
Like all agents involved, he has been the target of much speculation and criticism for his actions on that day.
Countering the criticism, the organist, jazz-pianist, and composer Henrik Sørensen defended the free improvisational form used by Magle on Like a Flame in an article in Danish organ-magazine Orgelforum.
This 22 second clip of Nirvana's Smells Like Teen Spirit is used for the purposes of criticism and comment on the band Nirvana.
Like his father, Debayle had little tolerance for the heavy criticism against his regime deriving from La Prensa, who continuously argued for responsible government, participator democracy, and liberal economic policies.
Like many, Krauss had been drawn to the criticism of Clement Greenberg, as a counterweight to the highly subjective, poetic approach of Harold Rosenberg.
Like many high-profile referees in top-flight football, Rennie has attracted criticism from within the game.

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