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 ").

As such it draws to a conclusion the themes introduced in Genesis and played out in Exodus and Leviticus: God has promised the Israelites that they shall become a great ( i. e. numerous ) nation, that they will have a special relationship with Yahweh their god, and that they shall take possession of the land of Canaan.

Forty years before the destruction of the Temple in Jerusalem in 70, i. e. in 30, the Sanhedrin effectively abolished capital punishment, making it a hypothetical upper limit on the severity of punishment, fitting in finality for God alone to use, not fallible people.

In the Christian Science textbook, Eddy cites seven synonyms for God: < i > Divine Principle, Life, Truth, Love, Soul, Spirit, and Mind .< i >< ref > Science & Health, Chapter 6 -- Science, Theology, Medicine, p. 115, < i >" Divine synonyms, GOD: Divine Principle, Life, Truth, Love, Soul, Spirit, Mind.

"</ i ></ ref > She calls the Holy Ghost " divine Science or the Holy Comforter ," the spiritual law of God operating as the Holy Ghost in the world.

They view their divine purpose as being ideally a " light upon the nations " and a " holy people " ( i. e., a people who live their lives fully in accordance with Divine will as an example to others ), not " the one path to God ".

One strong possibility is that it is a diptych ( i. e., divided into two parts ), with the division between parts 1 and 2 at the crossing of the Red Sea or at the beginning of the theophany ( appearance of God ) in chapter 19.

However, the majority of modern scholars view them as Jewish Christians, who taught that in order for pagans to belong to the people of God, they must be subject to some or all of the Jewish Law, ( i. e. Judaizers ).

Kalima is the declaration of faith, i. e. the professing that there is only one God ( Allah ) ( monotheism ) and that Muhammad is God's messenger.

God tells the patriarchs that he will be faithful to their descendants ( i. e. to Israel ), and Israel is expected to have faith in God and his promise.

Thus when God doth work, who shall let ( i. e. prevent ) it?

He removes the human sense of justice from his concept of God ; i. e., humanity is not the image of God: " To God all things are fair and good and just, but people hold some things wrong and some right.

Translated excerpts from Hezbollah's original 1985 manifesto read :< div > We are the sons of the umma ( Muslim community ) ...... We are an ummah linked to the Muslims of the whole world by the solid doctrinal and religious connection of Islam, whose message God wanted to be fulfilled by the Seal of the Prophets, i. e., Prophet Muhammad.

Several ships and one submarine of the Royal Navy have borne the name HMS Dreadnought in the expectation that they would " dread nought ", i. e. " fear nothing, but God ".

The Qur ' anic term for their religious doctrine is shirk ( i. e., " sharing "); it describes them as mushrikin ( i. e., those who believe in God, but " share " other Gods in divinity ).

* God redeems Israel ( i. e. the Jewish people ) from the captivity that began during the Babylonian Exile, in a new Exodus

* God creates a regent from the House of David ( i. e. the Messiah ) to lead the Jewish people and the world and usher in an age of justice and peace

If he does teshuva ( repentance ), i. e. he ceases his forbidden actions, regrets what he has done, apologizes to God, and makes a binding resolution never to repeat those actions, he is seen to be forgiven by God.

However, MUL and DIV are special cases, other arithmetic-logical instructions ( ADD, SUB, CMP, AND, OR, XOR, TEST ) may specify any of the eight registers EAX, ECX, EDX, EBX, ESP, EBP, ESI, EDI as the accumulator ( i. e. left operand and destination ); x86 is thus a fairly general register architecture, despite being based on an accumulator model.

Scoring occurs after all pieces ( generally 12 per player or team ) have been played, and is differential: i. e., the player or team with higher score is awarded the difference between the higher and lower scores for the round, thus only one team or player each round gains points.

The clear implication is that to bare one's throat would be tantamount to suicide ( which Jewish law forbids ) and it would also be considered helping a murderer kill someone and thus would " place an obstacle in front of a blind man " ( i. e., makes it easier for another person to falter in their ways ).

For lower frequencies of EMR up to those of visible light ( i. e., radio, microwave, infrared ), the damage done to cells and also to many ordinary materials under such conditions is determined mainly by heating effects, and thus by the radiation power.

* 1808 – Without a previous declaration of war, Russian troops cross the border to Sweden at Abborfors in eastern Finland, thus beginning the Finnish war, in which Sweden will lose the eastern half of the country ( i. e. Finland ) to Russia.

He was a member of the company of i Gelosi which Henry IV of France summoned to Paris to his bride, the young queen Marie de Medici, thus introducing the commedia dell ' arte style to France.

Criticizability, in contrast to falsifiability, and thus rationality, may be comprehensive ( i. e., have no logical limits ), though this claim is controversial even among proponents of Popper's philosophy and critical rationalism.

The conversion factor is 10 < sup > 8 </ sup >, since flux is the integral of field over an area, area having the units of the square of distance, thus 10 < sup > 4 </ sup > ( magnetic field conversion factor ) times the square of 10 < sup > 2 </ sup > ( linear distance conversion factor, i. e., centimetres per meter ).

During the gradual process by which Homo erectus made a transition from furry to naked skin, their hair texture putatively changed gradually from Afro-textured hair or ' kinky ' ( i. e. tightly coiled ) to straight hair ( the condition of most mammals, including humanity's closest cousins — chimpanzees ) This argument is based on the principle that curly hair impedes the passage of UV light into the body relative to straight hair ( thus curly or coiled hair would be particularly advantageous for dark-skinned hominids living at the equator ).

Older people are thus treated differently than younger people ( i. e., a distinction is made, discrimination occurs ).

Paul Maier states that the first case is generally seen as hopeless, given that a Jew, Josephus would not have claimed Jesus as the Messiah, and that the second option is hardly tenable given the presence of the reference in all Greek manuscripts ; thus a large majority of modern scholars accept the third alternative, i. e. partial authenticity.

Kennings of the type AB, where B routinely has the characteristic A and thus this AB is tautological, tends to mean " like B in that it has the characteristic A ", e. g. " shield-Njörðr ", tautological because the god Njörðr by nature has his own shield, means " like Njörðr in that he has a shield ", i. e. " warrior ".

Ping performs no packet processing ; it merely sends a response back when it receives a packet ( i. e. performs a no-op ), thus it is a relatively accurate way of measuring latency.

But it is intellectually handicapped, in that in combination with its telepathy, automatically assumes loss of ego when presented with a powerful telepathic feedback ( i. e. from a human ): It can assume a catatonic, unconscious state if a human it has telepathically linked thinks that it's just imagined a Nonesuch: thus the name.

There is a widespread use of the term in current popular literature, which replicates this error, i. e. that metaphysical means spiritual non-physical: thus, " metaphysical healing " means healing by means of remedies that are not physical.

It provided an ' atomic ' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts ( i. e. cannot be divided into smaller parts ) and thus the extreme end of a line is a point.

In light of this questioning of the canon of Scripture by Protestants in the 16th century, the ( Roman Catholic ) Council of Trent reaffirmed the traditional western canon ( i. e., the canon accepted at the 4th-century Council of Rome and Council of Carthage ), thus making the Canon of Trent and the Vulgate Bible dogma in the Catholic Church.

Mereological nihilism ( also called compositional nihilism ) is the position that objects with proper parts do not exist ( not only objects in space, but also objects existing in time do not have any temporal parts ), and only basic building blocks without parts exist, and thus the world we see and experience full of objects with parts is a product of human misperception ( i. e., if we could see clearly, we would not perceive compositive objects ).

Objectivism views government as " the means of placing the retaliatory use of physical force under objective control — i. e., under objectively defined laws ;" thus, government is both legitimate and critically important in order to protect individual rights.

The complex numbers also cannot be turned into an ordered field, as − 1 is a square ( of the imaginary number i ) and would thus be positive.

Classical economists on the contrary defined profit as what is left after subtracting costs except interest and risk coverage ; thus, if one leaves aside risk coverage for simplicity, the neoclassical zero-long-run-profit thesis would be re-expressed in classical parlance as profits coinciding with interest in the long period, i. e. the rate of profit tending to coincide with the rate of interest.

20S gate opening, and thus substrate degradation, requires the C-termini of the proteasomal ATPases, which contains a specific motif ( i. e., HbYX motif ).

Since we've assumed that we can infallibly identify programs for computing squares, we can determine whether t, which depends on a and i, is such a program, and that for every a and i ; thus we have obtained a program that decides whether program a halts on input i. Note that our halting-decision algorithm never executes t, but only passes its description to the squaring-identification program, which by assumption always terminates ; since the construction of the description of t can also be done in a way that always terminates, the halting-decision cannot fail to halt either.