For example, the proof that the column rank of a matrix over a field equals its row rank yields for matrices over division rings only that the left column rank equals its right row rank: it does not make sense to speak about the rank of a matrix over a division ring.

The boson matrix for SO ( 10 ) is found by taking the 15x15 matrix from the 10 + 5 representation of SU ( 5 ) and adding an extra row and column for the right handed neutrino.

However, Ludo played in the Indian Subcontinent has a resting place in each quadrant, normally the fourth square from the top in the right most column. These spaces are usually marked with a star.

* Measure ( typography ), in typography refers to the width of a block or column of text from the left margin to the right margin

Ramism could not exert any influence on the established Catholic schools and universities, which remained loyal to Scholasticism, or on the new Catholic schools and universities founded by members of the religious orders known as the Society of Jesus or the Oratorians, as can be seen in the Jesuit curriculum ( in use right up to the 19th century, across the Christian world ) known as the Ratio Studiorum ( that Claude Pavur, S. J., has recently translated into English, with the Latin text in the parallel column on each page ( St. Louis: Institute of Jesuit Sources, 2005 )).

An early printing of the Talmud ( Ta ' anit 9b ); Rashi's commentary is at the bottom of the right column, continuing for a few lines into the left column.

Each line of the text has some twelve to fourteen Greek uncial letters, arranged in four columns ( 48 lines in column ) with carefully chosen line breaks and slightly ragged right edges.

911 Memorials is a site that features the newest as they are added and provides a directory of each by community, state, and country in the column on the right of the site page.

3-M Littmann is also credited with a collapsible mold frame for sludge molding a single column bifurcating stethoscope tube with an internal septum dividing the single column stethoscope tube into discrete left and right binaural channels ( AKA " cardiology tubing "; including a covered, or internal leaf spring-binaural ear tube connector ).

The first column ( articles 3 – 11 ) constitutes rights of the individual, such as the right to life and the prohibition of slavery.

The Aramaic Testament of Levi ( DSS 4Q541 ) interprets in column 6: " God set right errors.

The technique requires that all vectors are augmented with a " 1 " at the end, and all matrices are augmented with an extra row of zeros at the bottom, an extra column — the translation vector — to the right, and a " 1 " in the lower right corner.

Mongolian text in Chinese transcription, with a glossary on the right of each column

Each vehicle would alternate its machine guns and / or cannon to the left or right respectively, firing continuously to cover the flanks on both sides of the column and suppress enemy counterfire.

Instead, a hammer was provided for every other column and the entire hammer bank was arranged to shift left and right, driven by another voice coil.

The vertical column of squares ( called files ) from White's left ( the queenside ) to his right ( the kingside ) are labeled a through h. The horizontal rows of squares ( called ranks ) are numbered 1 to 8 starting from White's side of the board.

Triglyphs were arranged regularly ; the last triglyph was centred upon the last column ( illustration, right: I .).

The church contains two first-class relics, the right wrist-bone of St. Paul and part of the column on which he was beheaded in Rome.

The right column illustrates why stationary states are called " stationary ".

Some Japanese crosswords are numbered from top to bottom down each column, starting with the leftmost column and proceeding right.

`` You'll stay right here '', commanded Bill Doolin, covering Red with his rifle.

Caesar himself commanded the cavalry, he posted the notorious tenth legion on his right under Sulla, with the undermanned eighth and possibly the ninth on his left under Antonius.

Marlborough took control of the left arm of the Allied forces including the attacks on Blenheim and Oberglauheim, whilst Eugene commanded the right including the attacks on Lutzingen.

* The right wing, composed of knights of Champagne and Burgundy, was commanded by the Duke of Burgundy Eudes and his lieutenants: III Gaucher de Châtillon Count of Saint-Pol, Count Wilhelm I of Sancerre, Count of Beaumont and Mathieu de Montmorency and Adam II Viscount of Melun.

Mark Antony and Gellius Publicola commanded the right wing of the Antonian fleet, while Marcus Octavius and Marcus Insteius commanded the centre, with Cleopatra's squadron positioned behind them.

Negus Tekle Haymanot commanded the right wing, Ras Alula the left, and Rasses Makonnen and Mengesha the center, with Ras Mikael at the head of the Oromo cavalry ; the Emperor and his consort remained with the reserve.

Antony commanded Italy whilst Caesar destroyed Pompey's legions in Spain, and led the reinforcements to Greece, before commanding the right wing of Caesar's armies at Pharsalus.

Saladin played a major role, commanding the right wing of the Zengid army, while a force of Kurds commanded the left, and Shirkuh stationed in the center.

The king commanded the centre of his army, with Alan of Brittany on his right and William of Aumale on his left.

The French right wing, commanded by MacMahon and accompanied by Napoleon III himself, attempted to relieve Bazaine but was itself surrounded and trapped by the Germans in the disastrous Battle of Sedan on August 31.

The French Army of the Rhine, commanded by Marshal François-Achille Bazaine, numbering about 183 infantry battalions, 104 cavalry squadrons, backed by 520 heavy cannon, totaling 112, 800 officers and men, dug in along high ground with their southern left flank at the town of Rozerieulles, and their northern right flank at St. Privat.

Beginning in late April, a Union force of 100, 000 moved slowly against Corinth, under Halleck's command with Grant relegated to second-in-command ; Sherman commanded the division on the extreme right of the Union's right wing ( under George H. Thomas ).

The royalist army, perhaps as much as twice the size of Montfort's, was led by Edward on the right and the King's brother Richard of Cornwall on the left, while the King himself commanded the central battalion.

The right battle was commanded by the Duke of Somerset.

Marion commanded the right wing under General Greene at the Battle of Eutaw Springs.

The stronger contingent was on the Macedonian right, where Perseus commanded the heavy cavalry ( including his elite Sacred Squadron ), and the Thracian Odrysian cavalry were deployed.

The king commanded the centre of his army, with Alan of Brittany on his right and William of Aumale on his left.

Behind them on the right of the second line, Sir Richard England led his 3rd Division while on his left the Duke of Cambridge commanded the 1st Division.

After the French right wing was in position ( commanded by Luxembourg himself ), their artillery opened fire at about 10: 00, striking the Allied infantry with great effect.

Lieutenant General Eugenio Navarro commanded the right flank division, whose positions included Collioure and Port-Vendres on the coast.

In the Battle of Zama ( 202 ) ( near modern-day Maktar, Tunisia ) Masinissa commanded the cavalry ( 6, 000 Numidian and 3, 000 Roman ) on Scipio's right wing, Scipio delayed the engagement for long enough to allow for Masinissa to join him.

Wellington himself commanded the small central force in a strategic feint, while Sir Thomas Graham conducted the bulk of the army around the French right flank over landscape considered impassable.