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 ").

* There exists a model of ZF ¬ C in which there is a function f from the real numbers to the real numbers such that f is not continuous at a, but f is sequentially continuous at a, i. e., for any sequence

The Aegean Sea (;, Aigaio Pelagos ; or historically ) is an elongated embayment of the Mediterranean Sea located between the southern Balkan and Anatolian peninsulas, i. e., between the mainlands of Greece and Turkey.

As researchers note, " a sense of ‘ responsibility ,’ or self agency, in a context of uncertainty ( probabilistic outcomes ) drives the neural system underlying appetitive motivation ( i. e., nucleus accumbens ) more strongly in temperamentally inhibited than noninhibited adolescents.

An analog or analogue signal is any continuous signal for which the time varying feature ( variable ) of the signal is a representation of some other time varying quantity, i. e., analogous to another time varying signal.

The primary disadvantage of analog signaling is that any system has noise – i. e., random unwanted variation.

For the incremental case ( i. e., ), this simplifies to:

Almonds are sold shelled ( i. e., after the shells are removed ), or unshelled ( i. e., with the shells still attached ).

As far as atoms and their electron shells were concerned, not only did this yield a better overall description, i. e. the atomic orbital model, but it also provided a new theoretical basis for chemistry

It also guarantees the capacity to distinguish between false perceptions or illusions ( which are possible in perceptions of both the outer world and the inner world ) and true perceptions, or, better said, to distinguish in any perception between the influence of subjective elements ( i. e., viewpoint ) and the objective reality the perception points at.

In fact, the distribution of the sample mean will be equal to the distribution of the samples themselves ; i. e., the sample mean of a large sample is no better ( or worse ) an estimator of x < sub > 0 </ sub > than any single observation from the sample.

Together with better tools and enhanced technologies, this has led to new implementations of highly encoded and variable length designs without load-store limitations ( i. e. non-RISC ).

All of these agents share the property of being quite hydrophobic ( i. e., as liquids, they are not freely miscible in water, and as gases they dissolve in oils better than in water ).

Over the last two decades, the evidence that better glycemic control ( i. e., keeping blood glucose and HbA1c levels as close to normal as possible ) reduces the rates of many complications of diabetes has become overwhelming.

The current state of psychological study about the nature of religiousness suggests that it is better to refer to religion as a largely invariant phenomenon that should be distinguished from cultural norms ( i. e. " religions ").

Knights rode in both the Muslim style, a la jineta ( i. e. the equivalent of a modern jockey's seat ), a short stirrup strap and bended knees allowed for better control and speed, or in the French style, a la brida, a long stirrup strap allowed for more security in the saddle ( i. e. the equivalent of the modern cavalry seat, which is more secure ) when acting as heavy cavalary.

Stoichiometry rests upon the very basic laws that help to understand it better, i. e., law of conservation of mass, the law of definite proportions ( i. e., the law of constant composition ) and the law of multiple proportions.

A game bid and made in a major suit ( i. e. 4 or 4 ) scores better than a game contract bid and made in a minor suit ( i. e. 5 or 5 ) or in notrump ( i. e. 3NT ).

# The hypothesis of indifference, i. e., that if there are supernatural beings they are indifferent to gratuitous evils, is a better explanation for ( 1 ) than theism.

If there is a new theory which is better at explaining and predicting phenomena than an older theory ( i. e. it has more explanatory power ), we are justified in believing that the newer theory describes reality more correctly.

The garage had a lien i. e. a " proprietary right or interest " in the car as security for the unpaid bill and this gave the garage a better right than the owner to possess the car at the relevant time.

Mill notes that, contrary to what its critics might say, there is “ no known Epicurean theory of life which does not assign to the pleasures of the intellect … a much higher value as pleasures than to those of mere sensation .” However, he accepts that this is usually because the intellectual pleasures are thought to have circumstantial advantages, i. e. “ greater permanency, safety, uncostliness, & c .” Instead, Mill will argue that some pleasures are intrinsically better than others.

The UNU Institute for Water, Environment and Health ( Hamilton, Ontario, Canada ) works directly on the global water crisis., The three core functions of UNU-INWEH are: ( i ) helping developing countries meet the Millennium Development Goals through capacity development: ( ii ) facilitating global knowledge enhancement and networking to address the global water crisis ; and ( iii ) fostering better approaches to water management and governance through applied research designed to fill critical policy gaps

Specifically, the weather must be better than basic VFR weather minima, i. e. in visual meteorological conditions ( VMC ), as specified in the rules of the relevant aviation authority.

Douglass sought to better understand cycles of sunspot activity and reasoned that changes in solar activity would affect climate patterns on earth which would subsequently be recorded by tree-ring growth patterns ( i. e., sunspots → climate → tree rings ).

In the classic version of the game, collaboration is dominated by betrayal ( i. e. betrayal always produces a better outcome ) and so the only possible outcome is for both prisoners to betray the other.

It proved better than Z-buffer / painter's type algorithms at handling scenes of high depth complexity with costly pixel operations ( i. e. perspective-correct texture mapping without hardware assist ).

On high-traction surfaces such as bitumen, or concrete, many ( though not all ) ABS-equipped cars are able to attain braking distances better ( i. e. shorter ) than those that would be easily possible without the benefit of ABS.

Bytecode may often be either directly executed on a virtual machine ( i. e. interpreter ), or it may be further compiled into machine code for better performance.