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* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then
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If and is
If the circumstances are faced frankly it is not reasonable to expect this to be true.
If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.
If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.
If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;
If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.
If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.
If it is an honest feeling, then why should she not yield to it??
If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.
If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.
If he is good, he may not be legal ; ;
If the man on the sidewalk is surprised at this question, it has served as an exclamation.
If the existent form is to be retained new factors that reinforce it must be introduced into the situation.
If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
If he is a traditionalist, he is an eclectic traditionalist.
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.
If and norm
If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.
If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.
* If is the norm ( usually noted as ) defined in the square-summable sequence space ℓ < sup > 2 </ sup > ( which also matches the usual distance in a continuous and isotropic cartesian space ), then
If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).
If they further reflect, they must also recognize that an act of mutual love which impairs the capacity to transmit life which God the Creator, through specific laws, has built into it, frustrates His design which constitutes the norm of marriage, and contradicts the will of the Author of life.
If ( V, ‖·‖) is a normed vector space, the norm ‖·‖ induces a metric ( a notion of distance ) and therefore a topology on V. This metric is defined in the natural way: the distance between two vectors u and v is given by ‖ u − v ‖.
If has finite norm, then is infinitely close to.
If X and Y are subsets of the real numbers, d < sub > 1 </ sub > and d < sub > 2 </ sub > can be the standard Euclidean norm, || · ||, yielding the definition: for all ε > 0 there exists a δ > 0 such that for all x, y ∈ X, | x − y | < δ implies | f ( x ) − f ( y )| < ε.
If X is a normed space, then the dual space X * is itself a normed vector space by using the norm ǁφǁ = sup < sub > ǁxǁ ≤ 1 </ sub >| φ ( x )|.
If the topology of the topological vector space is induced by a metric which is homogenous, as in the case of a metric induced by the norm of normed vector spaces, then the two definitions coincide.
If is a Gaussian integer whose norm is a prime number, then is a Gaussian prime, because the norm is multiplicative.
If we further consider both spaces with the sup norm the extension map becomes an isometry.
If we consider that its length is actually the distance from its tail to its tip, it becomes clear that the Euclidean norm of a vector is just a special case of Euclidean distance: the Euclidean distance between its tail and its tip.
If a is an ideal of O < sub > K </ sub >, other than the zero ideal we denote its norm by Na.
If Ishi were descended from both of the tribes and grew up with members of both, it may help explain his adaptive abilities, as his circumstances, essentially from birth, would have been different from the cultural norm of his people.
If we specifically choose the Euclidean norm on both R < sup > n </ sup > and R < sup > m </ sup >, then we obtain the matrix norm which to a given matrix A assigns the square root of the largest eigenvalue of the matrix A < sup >*</ sup > A ( where A < sup >*</ sup > denotes the conjugate transpose of A ).
If a peer group holds to a strong social norm, member will behave in ways predicted by their gender roles, but if there is not a unanimous peer agreement gender roles do not correlate with behavior
If we allow unbounded functions, this formula does not yield a norm or metric in a strict sense, although the obtained so-called extended metric still allows one to define a topology on the function space in question.
If x is orthogonal to y, then and the above equation for the norm of a sum becomes:
If and usually
If there are any major restrictions, they usually can be obtained in printed form.
If high accuracy is required in preflight leveling, it is usually necessary to integrate or doubly integrate the accelerometer outputs ( this also minimizes the noise problem ).
If you are not well acquainted with the area in which you wish to locate, or if you are not sure that you and your family will like and make a success of farming, usually you would do better to rent a place for a year or two before you buy.
If the intruder persisted, a biting lunge was usually launched at either the tail region or the naso-labial grooves.
If the defendant pleads guilty, an evidentiary hearing usually follows.
If this article / noun pair is used as the object of a verb, it ( usually ) changes to the accusative case, which entails an article shift in German – Ich sehe den Wagen.
If a cerebral AVM is detected before a stroke occurs, usually the arteries feeding blood into the nidus can be closed off to avert the danger.
If this special relationship does not exist then it not usually spoken of as " backward " compatibility but is instead just " compatible "— a consistent interface allowing interoperability between components and products that were each developed separately.
If diagnosed in time the various forms of plague are usually highly responsive to antibiotic therapy.
If the character encoding for a web page is chosen appropriately then HTML character references are usually only required for a markup delimiting characters mentioned above, and for a few special characters ( or not at all if a native Unicode encoding like UTF-8 is used ).
If more than one wavelength is present ( as is usually the case ), one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity.
If rain arrives, it is usually between August and October.
If the decrease during exhalation drops the heart rate below 60 bpm on each breath, this type of bradycardia is usually deemed benign and a sign of good autonomic tone.
If more than one eigenvalue is negative, then the stationary point is a more complex one, and is usually of little interest.
If the shooter " hits " the point value again ( any value of the dice that sum to the point will do ; the shooter doesn't have to exactly repeat the value combination of the come-out roll ) before rolling a seven, the Pass line wins and a new round starts, usually with the dice staying with the current shooter.
If a die leaves the table, the shooter will usually be asked to select another die from the remaining three but can request using the same die if it passes the boxman's inspection.
If a non-working point number placed, bought or laid becomes the new point as the result of a come-out, the bet is usually refunded, or can be moved to another number for free.
If a player is unsure of whether a bet is a single or multi-roll bet, it can be noted that all single-roll bets will be displayed on the playing surface in one color ( usually red ), while all multi-roll bets will be displayed in a different color ( usually yellow ).
If one set is played, the pieces usually go into the opponent's starting corner, and the number of pieces per side is often increased to 15 ( instead of the usual 10 ).
If three sets are played, the pieces usually go into the opponent's starting corners.
If Fulham win the toss, they usually choose to play towards the Hammersmith End in the second half.
If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.
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