The diagonalizable operator is the special case of this in which Af for each i.

For each i, let Af.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

The family moved north across the Ohio River to free ( i. e., non-slave ) territory and made a new start in what was then Perry County but is now Spencer County, Indiana.

This religion preaches the view of Ahimsa – to live and let live, thereby not harming sentient beings, i. e. uncompromising reverence for all life.

The importance lies in sacrifice for the sake of the greater good ; Islam considers those practicing i ' thar as abiding by the highest degree of nobility.

This is similar to the notion of chivalry, but unlike that European concept, in i ' thar attention is focused on everything in existence.

A constant concern for Allah ( i. e. God ) results in a careful attitude towards people, animals, and other things in this world.

This concept was emphasized by Sufi mystics like Rabia al-Adawiyya who paid attention to the difference between dedication to Allah ( i. e. God ) and dedication to people.

For many Muslims, i ' thar must be practiced as a religious obligation during specific Islamic holidays.

However, i ' thar is also still an Islamic ideal to which all Muslims should strive to adhere at all times.

These two defunct phyla were the Myxomycota ( i. e., plasmodial slime molds, now classified in the taxon Myxogastria ), and Acrasiomycota ( i. e. cellular slime molds, now divided into the taxa Acrasida and Dictyosteliida ).

Compared to earlier telegraph codes, the proposed Bell code and ASCII were both ordered for more convenient sorting ( i. e., alphabetization ) of lists and added features for devices other than teleprinters.

* Philostratus the Elder, Images i. 24 Hyacinthus ( 170 – 245 CE )

The Extrasolar Planets Encyclopaedia includes objects up to 25 Jupiter masses, saying, " The fact that there is no special feature around 13 MJup in the observed mass spectrum reinforces the choice to forget this mass limit ," and the Exoplanet Data Explorer includes objects up to 24 Jupiter masses with the advisory: " The 13 Jupiter-mass distinction by the IAU Working Group is physically unmotivated for planets with rocky cores, and observationally problematic due to the sin i ambiguity.

He dictates 24 books for the public ( i. e. the Hebrew Bible ) and another 70 for the wise alone ( 70 unnamed revelatory works ).

In the Kashmir Valley, the Hindus represented " 524 in every 10, 000 of the population ( i. e. 5. 24 %), and in the frontier wazarats of Ladhakh and Gilgit only 94 out of every 10, 000 persons ( 0. 94 %).

Then the data are passed through high-performance restartable dithering engine which is used regardless of monitor bit depth, i. e. also for 24 bits per pixel colour.

Meanwhile, Pausanias ( i. 24. 7 ) merely noted the subject and moved on.

For pure rocket approaches Tsiolkovsky's rocket equation shows that dead weight will prevent reaching orbit unless the ratio of propellant to structural mass ( called mass ratio ) is very high — between about 10 and 25 ( i. e. 24 parts propellant weight to 1 part structural weight ; depending on propellant choice ).

* March 24 – For the only time in history, the Boat Race between the Universities of Cambridge and Oxford is declared a " dead heat " ( i. e. a draw ).

To help compare sizes of different surface areas, we list here areas between 10 < sup > 18 </ sup > square metres and 10 < sup > 24 </ sup > square metres, i. e. those between 1 trillion km < sup > 2 </ sup > and 1 quintillion km < sup > 2 </ sup >.

Several ruby-set pieces were included in the sale, notably a ring set with an 8. 24 ct gem that broke the ' price-per-carat ' record for rubies ($ 512, 925 per carat, i. e. over $ 4. 2 million in total ), and a necklace that sold for over $ 3. 7 million.

In order to keep track of the time of day, a clock must be at the same point at the same time each day, i. e. repeat every 24 hours.

Dental subluxation is a non-dental-urgency condition, i. e., unlikely to result in significant morbidity if not seen within 24 hours by a dentist, and usually treated conservatively ; good oral hygiene with 0. 12 % chlorhexidine gluconate mouthwash, a soft and cold diet, and avoidance of smoking for several days.

Longchen Rabjampa was born at Gra-phu stod-gron in g. Yo-ru in Eastern dBus in Central Tibet on the eighth day of the second lunar month of the Earth-Male-Ape year ( i. e., Friday, 1 March 1308 ; which was at the beginning of that Tibetan calendrical year ) The date of Longchen Rabjampa's ' parinirvāṇa ' was on the eighteenth day of the twelfth lunar month of the Water-Female-Hare year ( i. e., Wednesday, 24 January 1364 ; which was at the end of that Tibetan calendrical year ) at O-rgyan-rdzong in Gangs-ri thod-kar, Tibet.

The film is also shortened by being run at ' sound speed ', i. e. 24 frames per second ; like most silent movies it was originally shot and exhibited at a slower speed.

For a demonstration, look closely at the following picture ( note: this will work only on monitors displaying true color, i. e., 24 or 32 bits ) where dark shades of red, green and blue are shown using 128 levels of intensities for each component ( 7 bits ).

For such an orbital to reproduce the equivalent to the Earth's gravity ( i. e. 9. 8 Newtons / kg at sea level ), whilst maintaining Earth's 24 hour period of rotation, it would need to have a diameter of approximately 3. 71 million kilometres.

In the CDP the population was spread out with 23 % under the age of 18, 4 % from 18 to 24 ( i. e., 44 individuals ), 21 % from 25 to 44, 34 % from 45 to 64, and 18 % who were 65 years of age or older.

All other rules for determining hand value are as in the suit game ( i. e. the base value of 24 is multiplied by the game level, as described above ).

There are indeed certain exceptions ; Basilides taught the existence of a " great archon " called Abraxas who presided over 365 archons ( Irenaeus, Adversus Haereses, i. 24 ); in the Valentinian system, the Seven are in a manner replaced by the Aeons.

The computational power of this processor, i. e. its performance, is estimated as 10, 000 MIPS, which is about 24 times higher than the estimated performance of its predecessor, the Audigy processor.

During treatment of hyponatremia, the serum sodium should not be allowed to rise by more than 8 mmol / l over 24 hours ( i. e. 0. 33 mmol / l / h rate of rise ).

For the most part, the dimensions of these image sensors are similar to the APS-C image frame size, i. e., approximately 24 mm x 16 mm.

The technical term for slow motion is overcranking which refers to the concept of cranking a handcranked camera at a faster rate than normal ( i. e. faster than 24 frames per second ).

An applet typically also refers to Java applets, i. e., programs written in the Java programming language that are included in a web page.

Allotropy refers only to different forms of an element within the same phase ( i. e. different solid, liquid or gas forms ); the changes of state between solid, liquid and gas in themselves are not considered allotropy.

Similarly, one declarative sentence can refer to many propositions ; for instance, " I am hungry " changes meaning ( i. e. refers to different propositions ) depending on the person uttering it.

** The breech refers to the mass of solid metal behind the bottom of the bore extending to the base of the breech and including the base ring ; it also generally refers to the end of the cannon opposite the muzzle, i. e., the location where the explosion of the gunpowder begins as opposed to the opening through which the pressurized gas escapes.

" " Framing " refers to conceptualizing the problem, i. e., defining goals and objectives.

Note that the first element in a sequence has the index one and that $ refers to the length ( i. e. total number of elements ) of the sequence.

Sensitivity refers to the ease with which an explosive can be ignited or detonated, i. e., the amount and intensity of shock, friction, or heat that is required.

However, in the context of explosives, stability commonly refers to ease of detonation, which is concerned with kinetics ( i. e., rate of decomposition ).

The original title of the film, Fucking Åmål, refers to the girls ' feelings about their smalltown home: in a key scene one of the girls shouts in desperation " varför måste vi bo i fucking jävla kuk-Åmål " ( which roughly translates to " why do we have to live in fucking bloody cock-Åmål ").

Functional decomposition refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed ( i. e., recomposed ) from those parts by function composition.

* Plus quam perfectum (= relative past, i. e. a past that refers to the past of a reference in the past )

* Anterior Futurus (= relative future, i. e. a past that refers to the past of a future point )

Generally speaking, the term ' invisibles ' refers to both ; international payments for services ( as opposed to goods ) as well as movements of money for which there is no contra transaction ( i. e. money is not exchanged for either a good or a service ).

The Against Marcion is lost, as is the Refutation of all Heresies to which Justin himself refers in Apology, i. 26 ; Hegesippus, besides perhaps Irenaeus and Tertullian, seems to have used it.

A matrix generally refers to a 2-dimensional array, i. e. an m × n array where m and n are greater than 1.

The term " malt " refers to several products of the process: the grains to which this process has been applied, for example malted barley ; the sugar, heavy in maltose, derived from such grains, such as the baker's malt used in various cereals ; or a product based on malted milk, similar to a malted milkshake ( i. e., " malts ").

NATO refers to surface-to-air missile systems mounted on ships or submarines with the same names as the corresponding land-based systems, but the US DoD assigns a different series of numbers with a different suffix ( i. e., SA-N-vs. SA -) for these systems.

Originally, the term referred to the presiding officer of a ceremony or meeting ( i. e., chairman ), but today it most commonly refers to an official.

Tangible personal property refers to any type of property that can generally be moved ( i. e., it is not attached to real property or land ), touched or felt.

Quality of service sometimes refers to the level of quality of service, i. e. the guaranteed service quality.

There, it refers to the wavelength at which the material dispersion is minimum, i. e. essentially zero.

Similarly, the manual for the ORCA / M assembler refers to a field indicating the order of the bytes in a number field as, and the Mac OS X operating system refers to " byte sex " in its compiler tools .</ ref > The usual contrast is whether the most significant or least significant byte is ordered first — i. e., at the lowest byte address — within the larger data item.