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.

Like other character encodings, ASCII specifies a correspondence between digital bit patterns and character symbols ( i. e. graphemes and control characters ).

; Balanced design: An experimental design where all cells ( i. e. treatment combinations ) have the same number of observations.

Alkanes ( also known as paraffins or saturated hydrocarbons ) are chemical compounds that consist only of hydrogen and carbon atoms and are bonded exclusively by single bonds ( i. e., they are saturated compounds ) without any cycles ( or loops ; i. e., cyclic structure ).

Saturated hydrocarbons can also combine any of the linear, cyclic ( e. g., polycyclic ) and branching structures, and they are still alkanes ( no general formula ) as long as they are acyclic ( i. e., having no loops ). They also have single covalent bonds between their carbons.

If the appellate court does find a legal defect in the decision " below " ( i. e., in the lower court ), it may " modify " the ruling to correct the defect, or it may nullify (" reverse " or " vacate ") the whole decision or any part of it.

In German, words starting with sch-( constituting the German phoneme ) would be intercalated between words with initial sca-and sci-( all incidentally loanwords ) instead of this graphic cluster appearing after the letter s, as though it were a single letter — a lexicographical policy which would be de rigueur in a dictionary of Albanian, i. e. dh -, ë -, gj -, ll -, rr -, th -, xh-and zh-( all representing phonemes and considered separate single letters ) would follow the letters d, e, g, l, n, r, t, x and z respectively.

This led to the conclusion ( Moseley's law ) that the atomic number does closely correspond ( with an offset of one unit for K-lines, in Moseley's work ) to the calculated electric charge of the nucleus, i. e. the proton number Z.

An argument of this form is invalid, i. e., the conclusion can be false even when statements 1 and 2 are true.

* In the year 1000, the Icelander Leif Ericson was the first European to set foot on North American soil, corresponding to today's Eastern coast of Canada, i. e. the province of Newfoundland and Labrador, including the area of land named " Vinland " by Ericson.

The practical definition may lead to confusion with the definition of a coulomb ( i. e., 1 amp-second ), but in practical terms this means that measures of a constant current ( e. g., the nominal flow of charge per second through a simple circuit ) will be defined in amperes ( e. g., " a 20 mA circuit ") and the flow of charge through a circuit over a period of time will be defined in coulombs ( e. g., " a variable-current circuit that flows a total of 10 coulombs over 5 seconds ").

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

* Key size, i. e., the size of key used to encrypt a message.

The size of a display is usually by monitor manufacturers given by the diagonal, i. e. the distance between two opposite screen corners.

0. 01 torr is one order of magnitude above high vacuum, where fluids are in the free molecular flow regime, i. e. the mean free path of molecules is comparable to the size of the equipment.

The number of elements in a sequence is not fixed ( i. e. the size of the vector / array does not have to be declared ).

The primary benefit promised by ECC is a smaller key size, reducing storage and transmission requirements — i. e., that an elliptic curve group could provide the same level of security afforded by an RSA-based system with a large modulus and correspondingly larger key — e. g., a 256bit ECC public key should provide comparable security to a 3072bit RSA public key ( see # Key sizes ).

Therefore, local changes in concentration ( i. e. creaming ) and global changes in size ( i. e. flocculation, coalescence ) can be detected and monitored.

First we consider fields where the size is prime, i. e., n = 1.

Next we consider fields where the size is not prime, but is a prime power, i. e., n > 1.

A plot of the first few factorials makes clear that such a curve can be drawn, but it would be preferable to have a formula that precisely describes the curve, in which the number of operations does not depend on the size of n. The simple formula for the factorial, n < nowiki >!</ nowiki > = 1 × 2 × … × n, cannot be used directly for fractional values of n since it is only valid when n is a natural number ( i. e., a positive integer ).

The letter is followed by a three-digit number ; the first digit indicates the NOAA " class " ( i. e., size ) of the vessel, which NOAA assigns based on the ship's gross tonnage and horsepower, while the next two digits combine with the first digit to create a unique three-digit identifying number for the ship.

Depending on the density, size and temperature of a given cloud, the hydrogen in it can be neutral ( H I regions ), ionized ( H II regions ) ( i. e. a plasma ), or molecular ( molecular clouds ).

( Note: Some older operating systems may handle such values incorrectly ( i. e., signed instead of unsigned ), which would make it impossible to access files larger than 2 GB in size.

If a large, b-bit number is the product of two primes that are roughly the same size, then no algorithm has been published that can factor in polynomial time, i. e., that can factor it in time O ( b < sup > k </ sup >) for some constant k. There are published algorithms that are faster than O (( 1 + ε )< sup > b </ sup >) for all positive ε, i. e., sub-exponential.

It is a connected Lie group that cannot be faithfully represented by matrices of finite size, i. e., a nonlinear group.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

Though the title " abbot " is not given in the Western Church to any but actual abbots of monasteries today, the title archimandrite is given to " monastics " ( i. e., celibate ) priests in the East, even when not attached to a monastery, as an honor for service, similar to the title of monsignor in the Western / Latin Rite of the Roman Catholic Church.

Alpha particles have a typical kinetic energy of 5 MeV ( that is, ≈ 0. 13 % of their total energy, i. e. 110 TJ / kg ) and a speed of 15, 000 km / s.

It was at Anah that the emperor Julian met the first opposition on his disastrous expedition against Persia ( 363 ), when he got possession of the place and transported the people ; and there that Ziyad and Shureih with the advanced guard of Ali's army were refused passage across the Euphrates ( 36 / 657 ) to join Ali in Mesopotamia ( Tabari i. 3261 ).

When non-native speakers speak Hindi-Urdu, they might pronounce / व / in ' व ् रत ' as, i. e. as wrat instead of the correct vrat.

Antigenicity is the ability to combine specifically with the final products of the immune response ( i. e. secreted antibodies and / or surface receptors on T-cells ).

* Auxiliary Storage Pool, a group of disk drives in the IBM i ( aka OS / 400 ) operating system

Originally released for the IBM 6150 RISC workstation, AIX now supports or has supported a wide variety of hardware platforms, including the IBM RS / 6000 series and later IBM POWER and PowerPC-based systems, IBM System i, System / 370 mainframes, PS / 2 personal computers, and the Apple Network Server.

In abstract algebra, a field extension L / K is called algebraic if every element of L is algebraic over K, i. e. if every element of L is a root of some non-zero polynomial with coefficients in K. Field extensions that are not algebraic, i. e. which contain transcendental elements, are called transcendental.

To maintain network performance, networks may apply traffic policing to virtual circuits to limit them to their traffic contracts at the entry points to the network, i. e. the User – network interfaces ( UNIs ) and Network-to-network interfaces ( NNIs ): Usage / Network Parameter Control ( UPC and NPC ).

The dental formula was i. 0 / 3, c. 1 / 1, p. 3 / 3 · 4, m. 3 / 3, the upper canines having been long sabre-like weapons, protected by a descending flange on each side of the lower front jaw.

In general, the difference between a statistics program and a biostatistics program is twofold: ( i ) statistics departments will often host theoretical / methodological research which are less common in biostatistics programs and ( ii ) statistics departments have lines of research that may include biomedical applications but also other areas such as industry ( quality control ), business and economics and biological areas other than medicine.

Small could mean less than 3 dB below ( i. e., power output < 1 / 2 or voltage output < 0. 707 of ) the maximum value, or more rarely 10 dB below, or it could mean below a certain absolute value.

The Boltzmann distribution for the fractional number of particles N < sub > i </ sub > / N occupying a set of states i possessing energy E < sub > i </ sub > is:

The D82 could have up to 32, 768 words of core memory and continued the use of separate instruction and i / o processors.

Given any expression involving complex numbers, bras, kets, inner products, outer products, and / or linear operators ( but not addition ), written in bra-ket notation, the parenthetical groupings do not matter ( i. e., the associative property holds ).