Note that the tensor rank of a matrix can also mean the minimum number of simple tensors necessary to express the matrix as a linear combination, and that this definition does agree with matrix rank as here discussed.

Note that the number of non-zero is exactly the rank of the matrix.

Note that the IDF uses this rank across all three of its services.

Note that although many air forces use the rank of second lieutenant, in most Commonwealth air forces the equivalent rank of pilot officer is used.

* Artesh-bod ( Iran ) ( Note: Since the Islamic Revolution of 1979 no one has been promoted to this rank.

Note: Before unification in 1968 of the Royal Canadian Air Force, Canadian Army, and the Royal Canadian Navy, rank structure and insignia followed the British pattern.

Note the first edition has Fairbairn ’ s rank as ‘ Captain ’ all subsequent ( 1940's ) editions as ‘ Major ’.

Note crimson shoes ( buty karmazynowe ), a sign of wealth and rank ( magnates nickname were ' karmazyni ' - the crimson ones-because of those boots.

Note that the German inscription names his rank as oberst ( colonel ).

Note that the Wehrmacht and SS rank of Generalleutnant was equivalent to the rank of major general in the U. S. and British armies, as well as other western militaries.

Note: The second rank of Lance Corporal, formerly " Private ", was changed in January 2010, due to the French translation " Soldat " being the word " soldier ".

Note: This story is set in the days before Gordon achieved the rank of police commissioner, and Bullock the rank of detective.

Note that there is doubt about rank equivalency in countries that have Fleet Admirals but no Commodores, such as the former German Empire and Russia-often it is considered that in these countries a Fleet Admiral equates to an OF-9 rank, an Admiral to OF-8, a Vice Admiral to OF-7, and a Counter / Rear Admiral to OF-6 ( i. e. the ranks all move down one grade ).

Note that there is doubt about rank equivalency in countries that have no brigadier-generals but both colonel-generals and full generals, such as the German Empire and Russia-often it is considered that in these countries a colonel-general equates to an OF-9 rank, a general to OF-8, a lieutenant-general to OF-7, and a major-general to OF-6 ( i. e. the ranks below colonel-general all move down one grade ).

Note that the implementation as disjoint-set forests doesn't allow deletion of edges — even without path compression or the rank heuristic.

Note: This category treats " General " as an occupation, not a rank.

Note that there is doubt about rank equivalency in countries that have both colonel-generals and generals but no brigadier-generals, such as German Empire and Russia-often it is considered that in these countries a colonel-general equates to an OF-9 rank, a general to OF-8, a lieutenant-general to OF-7, and a major-general to OF-6 ( i. e. the ranks below colonel-general all move down one grade ).

Note heat sink and cooling fan assembly on rear side.

Note transfer table between erecting shops at rear of 20 acre plant.

Note that there are three almost entirely different pickup bodies for this generation of Falcon: the Australian Falcon Ute differed in having a shorter rear overhang than North American models, a cargo box that extended farther forward than the rear window, and shorter doors ; while the Argentinian version also shared the sedan's overall length and short " 4-door " doors, adding higher and more squared-off cargo box sides.

Note the firebox placed above the rear drivers.

Note that the Vanagon system was RWD-biased, due to the vehicle being rear-wheel drive by default ; the engine and transaxle were in the rear, whereas the viscous coupling was found in the front axle near the final drive.

Note the rear crew hatch, A frame and anchor.

Note that the rear of the Aura sits higher than the front.

Note the rod-actuated rear brake.

Note how much smaller the rear side windows are when compared to a stock Beetle.

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

Note, however, that it is six inches shorter at the forward end.

Note another piece of wood six inches wide is fastened to the transom between these pieces.

Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.

Note that the mass threshold is four times that of 1958 Alpha and that the flux is one fifth as large.

Note that the mass scale is one to two orders of magnitude greater than some previously used ; ;

Note also that if Af, then Af is divisible by the polynomial p, because Af contains each Af as a factor.

Note that flexural strength is not always improved by simply increasing the density, nor is the change always proportional from one formulation to another.

Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by

Note that this premise uses the phrase " is not ", a form of " to be "; this and many other examples show that he did not intend to abandon " to be " as such.

Note: This list is limited to linguists who have worked specifically on the Altaic problem since the publication of the first volume of Ramstedt's Einführung in 1952.

Note that any model of ZF ¬ C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true.

Note that there is no directly corresponding concept in the German language.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.

Note that this pressure increase is more than a simple 10: 1 compression ratio would indicate ; this is because the gas is not only compressed, but the work done to compress the gas has also heated the gas and the hotter gas will have a greater pressure even if the volume had not changed.

Note that this is not the same as a monophyly in which all descendants of a common ancestor are included.

Note: because Solar System bodies are never perfect diffuse reflectors, astronomers use empirically derived relationships to predict apparent magnitudes when accuracy is required.

Note that this is subtly different to the ' thanks ' list in the original BBC Model B.