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The determinant provides important information when the matrix is that of the coefficients of a system of linear equations, or when it corresponds to a linear transformation of a vector space: in the first case the system has a unique solution if and only if the determinant is nonzero, while in the second case that same condition means that the transformation has an inverse operation.
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determinant and provides
The starch source in a beer provides the fermentable material and is a key determinant of the strength and flavour of the beer.
The A-scan provides data on the length of the eye, which is a major determinant in common sight disorders.
determinant and important
He argued supply was easier to vary in longer runs, and thus became a more important determinant of price in the very long run.
The Congressional Budget Office ( CBO ) has written that " future growth in spending per beneficiary for Medicare and Medicaid — the federal government ’ s major health care programs — will be the most important determinant of long-term trends in federal spending.
This work is an important factor in determining the timbre of the guitar and a major determinant in the observation that rarely do two guitars ever sound alike, even though they are ostensibly identical in construction.
Recent research confirmed the X linked androgen receptor as the most important gene, with a gene on chromosome 20 being the second most important determinant gene ( snpedia ).
This polynomial encodes several important properties of the matrix, most notably its eigenvalues, its determinant and its trace.
Health care is conventionally regarded as an important determinant in promoting the general health and well-being of people around the world.
An important determinant of the success of production scheduling based on " pushing " the demand is the quality of the demand forecast that can receive such " push.
Shape of femoral head at the time when Legg-Calve Perthes Disease heals is the most important determinant of risk for degenerative arthritis ; hence, the shape of femoral head and congruence of hip are most useful outcome measures.
While many authorities suggest that an individual's style of throwing or the type of pitches they throw are the most important determinant of their likelihood to sustain an injury, the results of a 2002 study suggest that the total number of pitches thrown is the greatest determinant.
The elevation of the pinyon pine is an important determinant of the quantity of pine cone production, and therefore, will largely determine the amount of pine nuts the tree will yield.
The amount of fermentation time a wine spends in contact with grape skins is an important determinant of its resveratrol content.
In addition, the oxygen carrying capacity of the blood is also an important determinant of the equation.
Stroke volume is an important determinant of cardiac output, which is the product of stroke volume and heart rate, and is also used to calculate ejection fraction, which is stroke volume divided by end-diastolic volume.
Isolation, largely due to bad road infrastructure, has been found to be an important determinant of wealth and / or development in South Kivu.
The N-terminal amino acid of a protein is an important determinant of its half-life ( likelihood of being degraded ).
It is typical for large hills to split up pelotons, as the aerodynamic factors are much less important at slower climbing speeds and power-to-weight ratio is the key determinant of speed.
In general, the edge temperature under expected use is an important determinant of both composition and required heat treatment.
Economist David Foot of the University of Toronto concluded that the female's education is the most important determinant of the likelihood of her reproducing.
In all cases, the most important determinant of venom expenditure is generally the size of the snake, with larger specimens being capable of delivering much more venom.
Under proportional representation systems, district magnitude is an important determinant of the makeup of the elected body.
A clean water supply, especially so with regard to sewage, is the single most important determinant of public health.
determinant and information
* Hyman, Ray ; Stimulus information as a determinant of reaction time.
In Bayesian probability, the Jeffreys prior, named after Harold Jeffreys, is a non-informative ( objective ) prior distribution on parameter space that is proportional to the square root of the determinant of the Fisher information:
using the change of variables theorem, the definition of Fisher information, and that the product of determinants is the determinant of the matrix product:
* The eclipsing of monetary wealth by knowledge and information as the primary determinant of power and its distribution.
determinant and when
Thus a 2 × 2 matrix with determinant − 2, when applied to a region of the plane with finite area, will transform that region into one with twice the area, while reversing its orientation.
The entries can be numbers or expressions ( as happens when the determinant is used to define a characteristic polynomial ); the definition of the determinant depends only on the fact that they can be added and multiplied together in a commutative manner.
Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.
The determinant of a product AB is the product of the determinants of matrices A and B ( not defined when the underlying ring is not commutative ):
The determinant | S | of S, which is also called the resultant of the two polynomials, is 0 exactly when the two equations have a common solution in z.
While the role of K above in general Serre duality is played by the determinant line bundle of the cotangent bundle, when V is a manifold, in full generality K cannot merely be a single sheaf in the absence of some hypothesis of non-singularity on V. The formulation in full generality uses a derived category and Ext functors, to allow for the fact that K is now represented by a chain complex of sheaves, namely, the dualizing complex.
It is loft that is the primary determinant of the ascending trajectory of the golf ball, with the tangential angle of the clubhead's swing arc at impact being a secondary and relatively minor consideration ( though these small changes in swing angle can nevertheless have a significant influence on launch angle when using low-lofted clubs ).
These boundaries are nothing more than axial lines which are a feature that people are biased towards when relating to space ; for example one axial line determinant is gravity ( McNamara & Shelton, 2001 ; Kim & Penn, 2004 ).
The shift of a demand curve takes place when there is a change in any non-price determinant of demand, resulting in a new demand curve.
He concluded that this form of language evolved as a method of survival when clear communication might be the determinant of avoiding danger.
However, when a female determinant interacts with a male determinant of a different haplotype, no SI is created, and fertilization ensues.
The result is almost immediate when the matrix is seen to be the nth power of a matrix with determinant − 1:
These matrices arise naturally when using Dodgson condensation to compute a determinant.
A tensor density transforms as a tensor when passing from one coordinate system to another ( see classical treatment of tensors ), except that it is additionally multiplied or weighted by a power of the Jacobian determinant of the coordinate transition function or its absolute value.
Because the determinant can be negative, which it is for an orientation-reversing coordinate transformation, this formula is applicable only when W is an integer.
As noted by several researchers, attractiveness may not be the most influential determinant of personnel decisions, but may be a deciding factor when applicants possess similar levels of qualifications.
With respect to c, this is a homogeneous set of linear equations, which has a solution when the determinant of the coefficients to these unknowns is zero:
He was a determinant player when Nantes won the French Ligue 1 in 2001.
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