There are different types: QR decomposition, LQ, QL, RQ, RZ.

The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R ( also known as right-triangular ) and an orthogonal matrix Q.

* A reportable quantity ( RQ ) is the minimum quantity of a hazardous substance which, if released, is required to be reported.

This section applies to any facility which stores, produces or uses a " hazardous chemical " ( any chemical which is a physical hazard or a health hazard ) and releases a reportable quantity ( RQ ) of a substance contained in either of the following two tables published by the EPA in the Code of Federal Regulations:

The RQ is the critical number that determines if a release must be reported.

reported in 2002 that despite observing these increased oxidative biochemical adaptations to long-term endurance training ( similar to those mentioned above ), the AMPK response ( activation of AMPK with the onset of exercise ) to acute bouts of exercise decreased in red quadriceps ( RQ ) with training ( 3 – see Fig. 1 ).

* Grafton RQ, Hilborn R, Ridgeway L, Squires D, Williams M, Garcia S, Groves T, Joseph J, Kelleher K, Kompas T, Libecap G, Lundin CG, Makino M, Matthiasson T, McLoughlin R, Parma A, San Martin G, Satia B, Schmidt C-C, Tait M and Zhang LX ( 2008 ) " Positioning fisheries in a changing world " Marine Policy ( United Kingdom ), 32: 630-634.

* 2182: With an estimated probability of 0. 07 %, Apollo asteroid 1999 RQ < sub > 36 </ sub > could hit the Earth.

Analogously, we can define QL, RQ, and LQ decompositions, with L being a lower triangular matrix.

Conversely, the study did not observe the same results in white quadriceps ( WQ ) and soleus ( SOL ) muscles that they did in RQ.

In the following year ( 2011 ), open source satellite imagery showed Camp Lemmonier with a new drone apron supporting the RQ / MQ-1 PREDATOR.

This latter reaction is in accord with the reported decomposition of Af.

The small reaction occurring at 337-degrees-C is probably caused by decomposition of occluded nitrates, and perhaps by a small amount of some hydrous material other than Af.

The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.

If the direct-sum decomposition ( A ) is valid, how can we get hold of the projections Af associated with the decomposition??

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

In the primary decomposition theorem, it is not necessary that the vector space V be finite dimensional, nor is it necessary for parts ( A ) and ( B ) that P be the minimal polynomial for T.

# As exploratory data analysis, an ANOVA is an organization of an additive data decomposition, and its sums of squares indicate the variance of each component of the decomposition ( or, equivalently, each set of terms of a linear model ).

For example, the Banach – Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.

In the formation of an ordinary agate, it is probable that waters containing silica in solution — derived, perhaps, from the decomposition of some of the silicates in the lava itself — percolated through the rock and deposited a siliceous coating on the interior of the vapour-vesicles.

The first deposit on the wall of a cavity, forming the " skin " of the agate, is generally a dark greenish mineral substance, like celadonite, delessite or " green earth ", which are rich in iron probably derived from the decomposition of the augite in the enclosing volcanic rock.

The volatile hydride generated by the reaction that occurs is swept into the atomization chamber by an inert gas, where it undergoes decomposition.

If sugars are heated so that all water of crystallisation is driven off, then caramelization starts, with the sugar undergoing thermal decomposition with the formation of carbon, and other breakdown products producing caramel.

In fact, the decomposition of hydrogen peroxide is so slow that hydrogen peroxide solutions are commercially available.

The decomposition process is aided by shredding the plant matter, adding water and ensuring proper aeration by regularly turning the mixture.

A decomposition reaction is the opposite of a synthesis reaction, where a more complex substance breaks down into its more simple parts.

Pyrolysis gas chromatography mass spectrometry is a method of chemical analysis in which the sample is heated to decomposition to produce smaller molecules that are separated by gas chromatography and detected using mass spectrometry.

There are several methods for actually computing the QR decomposition, such as by means of the Gram – Schmidt process, Householder transformations, or Givens rotations.

QR decomposition is Gram – Schmidt orthogonalization of columns of A, started from the first column.

* The Iwasawa decomposition G = KAN of a semisimple group G as the product of compact, abelian, and nilpotent subgroups generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix ( a consequence of Gram – Schmidt orthogonalization ).

After the Gram matrix is learned by semidefinite programming, the output can be obtained via Cholesky decomposition.

Statements such as the Banach – Tarski paradox can be rephrased as conditional statements, for example, " If AC holds, the decomposition in the Banach – Tarski paradox exists.

* Hybrid Physical-Chemical Vapor Deposition ( HPCVD ) – This process involves both chemical decomposition of precursor gas and vaporization of a solid source.

All standard military explosives may be considered to have a high degree of stability at temperatures from – 10 to + 35 ° C, but each has a high temperature at which its rate of decomposition rapidly accelerates and stability is reduced.

This is similar ( but more categorical ) to concepts in group theory or module theory, where a given decomposition of an object into a direct sum is " not natural ", or rather " not unique ", as automorphisms exist that do not preserve the direct sum decomposition – see Structure theorem for finitely generated modules over a principal ideal domain # Uniqueness for example.

* A method applicable for particles without spin is to do a polar decomposition of the wavefunction and transform Schrödinger's equation into two coupled equations: the continuity equation from above and the Hamilton – Jacobi equation.

For any primary decomposition of I, the set of all radicals, that is, the set remains the same by the Lasker – Noether theorem.

Depending on the field of application, it is also named the discrete Karhunen – Loève transform ( KLT ), the Hotelling transform or proper orthogonal decomposition ( POD ).

In extremely dry or cold conditions, the normal process of decomposition is halted – by either lack of moisture or temperature controls on bacterial and enzymatic action – causing the body to be preserved as a mummy.

However, for composite sizes such as prime powers, the Cooley – Tukey FFT algorithm is much simpler and more practical to implement, so Rader's algorithm is typically only used for large-prime base cases of Cooley – Tukey's recursive decomposition of the DFT ( Frigo and Johnson, 2005 ).

The Dulmage – Mendelsohn decomposition is a structural decomposition of bipartite graphs that is useful in finding maximum matchings.

The Jordan – Chevalley decomposition expresses an operator as the sum of its semisimple ( i. e., diagonalizable ) part and its nilpotent part.

The Jordan normal form and the Jordan – Chevalley decomposition

* Comment: the Jordan normal form generalizes the eigendecomposition to cases where there are repeated eigenvalues and cannot be diagonalized, the Jordan – Chevalley decomposition does this without choosing a basis.

The Jordan – Chevalley decomposition is particularly simple on a basis on which the operator takes its Jordan normal form.

The vibrating image of the sun in Metzinger's painting, and so too of Delaunay's Paysage au disque ( 1906 – 1907 ), " is an homage to the decomposition of spectral light that lay at the heart of Neo-Impressionist color theory ..." ( Herbert, 1968 ) ( See, Jean Metzinger, Rijksmuseum Kröller-Müller, Otterlo )