On the other hand, the null space of Af and the null space of Af together span V, the former being the subspace spanned by Af and the latter the subspace spanned by Af and Af.

* V. Caston, 2011, Alexander of Aphrodisias: On Aristotle On the Soul.

On 15 September of the same year, Afonso V nullified all the laws and edicts approved under the regency.

On 8 November 1273, Andronikos II married Anne of Hungary ( 1260 – 1281 ), daughter of the king Stephen V of Hungary.

On 8 November 1273 Andronikos II married as his first wife Anna of Hungary, daughter of Stephen V of Hungary and Elizabeth the Cuman, with whom he had two sons:

On the death of Louis II in 1417 it reverted to Savoy, and, although Count René again retook the area for Provence in 1471, it had returned to Savoyard dominance by the start of the 16th century, by which point the County of Provence had become united with the Kingdom of France due to the death of Count Charles V in 1481.

Thirty years later, on March 6, 2009, Philips received an IEEE Milestone award with the following citation: " On 8 March 1979, N. V. Philips ' Gloeilampenfabrieken demonstrated for the international press a Compact Disc Audio Player.

On 9 October 1334, he confirmed the privileges granted to Jewish Poles in 1264 by Bolesław V the Chaste.

On reaching the intestinal wall, V. cholerae start producing the toxic proteins that give the infected person a watery diarrhea.

* On February 2, 2000, Philippe Binant, technical manager of Digital Cinema Project at Gaumont in France, realized the first digital cinema projection in Europe with the Texas Instruments mark V prototype projector.

* On the Question of Dialectics, V. I.

* Louis V. King On The Direct Numerical Calculation Of Elliptic Functions And Integrals ( Cambridge University Press, 1924 )

On 5 December 1719, with Philip V fast becoming the common enemy of all Europe, Alberoni was ordered to leave Spain, Elizabeth herself having taken an active part in procuring the decree of banishment.

On the eve of World War II, Soviet archives indicate a combined camp and colony population upwards of 1. 6 million in 1939, according to V. P. Kozlov.

* Aceituno, V., " On Information Security Paradigms ", ISSA Journal, September, 2005.

On 17 April 1934, French Foreign Minister Louis Barthou issued the so-called " Barthou note " which led to concerns on the part of Hitler that the French would ask for sanctions against Germany for violating Part V of the Versailles treaty.

On the right side, the visible portions of the loops are the verticals connecting two rows, arranged in a grid of V shapes.

On 9 April 1555, on the evening of the fourth day of the papal conclave, Cervini was " adored " as Pope, despite efforts by cardinals loyal to the Emperor Charles V to block his election.

On 7 January 1566, Ghislieri was elected to the Papal chair as Pope Pius V. He was crowned ten days later, on his 62nd birthday.

On 4 April 1312, a Crusade was promulgated by Pope Clement V at the Council of Vienne.

On his return to France, he immediately convened an assembly of French and Burgundian bishops at Vienne, where the imperial claim to a traditional lay investiture of the clergy was denounced as heretical and a sentence of excommunication was now pronounced against Henry V on the grounds that he had extorted the Privilegium from Paschal II by means of violence.

On a plot of torque versus runner speed, the torque curve is straight between these two points, ( 0, pQDV < sub > i </ sub >) and ( V < sub > i </ sub >, 0 ).

For example, a PLC might use 24 V DC I / O, with values above 22 V DC representing On, values below 2VDC representing Off, and intermediate values undefined.

Francis I of France recognizes Charles's claim to Naples, and Charles V, Holy Roman Emperor, recognizes Francis's claim to Milan.

* 1521 – Martin Luther's first appearance before the Diet of Worms to be examined by the Holy Roman Emperor Charles V and the other estates of the empire.

His restless and turbulent nature marked him out for a military career ; and having collected a small band of soldiers, he assisted Emperor Charles V in his war with France in 1543.

The dispute was referred to Emperor Charles V and other princes, but as no settlement was reached Albert continued his efforts to obtain help in view of a renewal of the war.

* 1111 – Henry V is crowned Holy Roman Emperor.

* Eudokia Angelina, who married ( 1 ) King Stefan I Prvovenčani of Serbia, then ( 2 ) Emperor Alexios V Doukas, and ( 3 ) Leo Sgouros, ruler of Corinth.

Alexios V Doukas, surnamed Mourtzouphlos (, d. December 1205, Constantinople ) was Byzantine Emperor ( 5 February – 12 April 1204 ) during the second and final siege of Constantinople by the participants of the Fourth Crusade.

There he saw " the things which have been sent to the king from the golden land "— the Aztec treasure that Hernán Cortés had sent home to Holy Roman Emperor Charles V following the fall of Mexico.

While Pope Stephen V supported Guy, crowning him Roman Emperor in 891, Arnulf threw his support behind Berengar.

Aldona had two daughters, Cunigunde ( died in 1357 ), who married Louis VI the Roman, the son of Louis IV, Holy Roman Emperor, on 1 January 1345, and Elisabeth ( died in 1361 ), who was married to Duke Bogislaus V of Pomerania.

* Charles V, Holy Roman Emperor ( 1500 – 1558 ), also Charles I of Spain

Under Pope Clement VII ( 1523 – 34 ), troops of the Catholic Holy Roman Emperor Charles V sacked Papal Rome in 1527, “ raping, killing, burning, stealing, the like had not been seen since the Vandals ”.

Pope Paul III then initiated several internal Church reforms while Emperor Charles V convened a meeting with Protestants in Regensburg, seat of the German diet, to reconcile differences.

Reopened at Trent on 1 May 1551 by convocation of Pope Julius III ( 1550 – 5 ), it was broken up by the sudden victory of Maurice, Elector of Saxony over the Emperor Charles V and his march into surrounding state of Tirol on 28 April 1552.

* Pirro Colonna, 16th century captain under Charles V, Holy Roman Emperor

In 1122, Henry V, Holy Roman Emperor entered into an agreement with Pope Calistus II known as the Concordat of Worms.

The Concordat of Worms, sometimes called the Pactum Calixtinum by papal historians, was an agreement between Pope Calixtus II and Holy Roman Emperor Henry V on September 23, 1122 near the city of Worms.

Following efforts by Lamberto Scannabecchi ( later Pope Honorius II ) and the Diet of Würzburg ( 1121 ) in 1122, Pope Calixtus II and Holy Roman Emperor Henry V entered into an agreement that effectively ended the Investiture Controversy.

Henry V was crowned by Pope Paschal II as the legitimate Holy Roman Emperor.

The daughters from this marriage were Cunigunde ( d. 1357 ), who was married to Louis VI the Roman, the son of Louis IV, Holy Roman Emperor, and Elisabeth, who was married to Duke Bogislaus V of Pomerania.

* Karl Brandi, The Emperor Charles V, 1939, pp185 – 8

His grandfather, Thomas Francis, founder of the Carignano line of the House of Savoy, was the son of Catherine Michelle – a daughter of Philip II of Spain – and the great-grandson of the Emperor Charles V. But of more immediate consequence to Leopold I was the fact that Eugene was the second cousin of Victor Amadeus, the Duke of Savoy, a connection that the Emperor hoped might prove useful in any future confrontation with France.

The last emperor to be crowned by the pope was Charles V ; all emperors after him were technically emperors-elect, but were universally referred to as Emperor.