# Calculate the eigenvectors and eigenvalues of the covariance matrix S. Each eigenvector has the same dimensionality ( number of components ) as the original images, and thus can itself be seen as an image.

In linear algebra, the Perron – Frobenius theorem, proved by and, asserts that a real square matrix with positive entries has a unique largest real eigenvalue and that the corresponding eigenvector has strictly positive components, and also asserts a similar statement for certain classes of nonnegative matrices.

In order to highlight the similarities and differences between the two cases the following points are to be noted: every non-negative matrix can be obviously obtained as a limit of positive matrices, thus one obtains the existence of an eigenvector with non-negative components ; obviously the corresponding eigenvalue will be non-negative and greater or equal in absolute value than all other eigenvalues.

The eigenvector corresponding to r has strictly positive components ( in contrast with the general case of non-negative matrices, where components are only non-negative ).

# A has a left eigenvector v with eigenvalue r whose components are all positive.

# Likewise, A has a right eigenvector w with eigenvalue r whose components are all positive.

Given a non-negative eigenvector v, and that at least one of its components say j-th is strictly positive, the corresponding eigenvalue is strictly positive, indeed, given n such that ( A < sup > n </ sup >)< sub > ii </ sub > > 0, hence: r < sup > n </ sup > v < sub > i </ sub >

An occupational therapist provides various means to these patients to restore or maintain their deteriorating performance components by using their residual capacities and capabilities to give them a sense of self-importance and a measure of confidence.

For an individual to give valid informed consent, three components must be present: disclosure, capacity and voluntariness.

Both genetic ( e. g., Berardinelli-Seip congenital lipodystrophy, Dunnigan familial partial lipodystrophy ) and acquired ( e. g., HIV-related lipodystrophy in patients treated with highly active antiretroviral therapy ) forms of lipodystrophy may give rise to severe insulin resistance and many of metabolic syndrome's components.

The auditory vesicle will give rise to the utricluar and saccular components of the membranous labyrinth.

The program has grown steadily to provide activities and projects for preschool through third grade as well as give educators an opportunity to build and certify a Nature Explore Outdoor Classroom using safe, durable, natural components.

Each of the components of the program is intended to give cadets the skills and knowledge that they will need for success as officers.

Metal or ceramic plates can be used with a soft vest, providing additional protection from rifle rounds, and metallic components or tightly woven fiber layers can give soft armor resistance to stab and slash attacks from knives and similar close-quarter weapons.

They have specific components, which in combinations can give rise to the variety to exist ( over 108 ), allowing different compositions to have different rhythms.

Certain operations on the strain tensor give the same result without regard to which orthonormal coordinate system is used to represent the components of strain.

However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation.

In addition, Gliessman highlighted that socio-economic, technological, and ecological components give rise to producer choices of food production systems.

This has been used to analyse stresses in aerospace and automotive components to give just two examples.

Where the traditional texts have both components, the silk texts frequently give only the phonetic half of the intended character.

* As a field of study, particularly, the study of the interactions between the components of biological systems, and how these interactions give rise to the function and behavior of that system ( for example, the enzymes and metabolites in a metabolic pathway ).

Although not the first comprehensive Chinese character dictionary ( the Erya predates it ), it was still the first to analyze the structure of the characters and to give the rationale behind them ( sometimes also the etymology of the words represented by them ), as well as the first to use the principle of organization by sections with shared components, called radicals ( bùshǒu 部首, lit.

Sarah Kofman asserts that these two components are crucial to a fuller understanding of the word, which has been historically translated and understood somewhat reductively: “ translators, who usually escape their perplexity by translating poros as ‘ expediency ’ and aporia as ‘ difficulty ’... leave the reader in the dark as to all the semantic richness of poros and aporia and give no hint as to their links with other words belonging to the same ‘ family ’” ( 9 ).

More pawls help spread the wear and give greater reliability although, unless the device is made to tolerances not normally found in bicycle components, simultaneous engagement of more than two pawls is rarely achieved.

In 1928, the company decided to give up radio manufacture and sold the factory and remaining components to another manufacturer.

The OpenMAX IL API strives to give media components portability across an array of platforms using the C-language.

Recent advances in bicycle components give the rider a wider range of gearing choices, allowing climbing specialists to use lower gears to ascend optimally while still having the higher gears necessary to keep up with other riders in the flatter sections.

Other components added into the circuit can give the performer more expressiveness, such as potentiometers, photoresistors ( for reaction to light ) and pressure sensors.

This is a favoured design where the torque is biased to the front wheels to give car-like handling, or where the maker wishes to produce both four-wheel drive and front-wheel drive cars with many shared components.

Differences in each of these three components give rise to different simulators.

Cray had always attacked the problem of increased speed with three simultaneous advances: more functional units to give the system higher parallelism, tighter packaging to decrease signal delays, and faster components to allow for a higher clock speed.

Sedimentation coefficients were computed as Af values and relative amounts of the various components were calculated from the Schlieren patterns.

While the appearance and relative existence of the leaf ceases, the components that formed the leaf become particulate material that goes on to form new plants.

Temperature dependence of the relative superfluid and normal components ρ < sub > n </ sub >/ ρ and ρ < sub > s </ sub >/ ρ as functions of T.

Cartilage is classified in three types, elastic cartilage, hyaline cartilage and fibrocartilage, which differ in the relative amounts of these three main components.

Statics is the branch of mechanics that is concerned with the analysis of loads ( force and torque, or " moment ") on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity.

The primary convention for expressing tacticity is in terms of the relative weight fraction of triad or higher-order components, as described above.

The space velocity relative to the Sun is about .< ref group =" nb "> The space velocity components are: U

Harmonic distortion may be expressed in terms of the relative strength of individual components, in decibels, or the Root Mean Square of all harmonic components: Total harmonic distortion ( THD ), as a percentage.

This leads to the formation of numerous new volatile aroma components, changes in relative amounts of aroma components in the wine, and the hydrolysis of components such as esters.

Additionally, the DJIA is criticized for being a price-weighted average, which gives higher-priced stocks more influence over the average than their lower-priced counterparts, but takes no account of the relative industry size or market capitalization of the components.

The waveplate is characterized by the amount of relative phase, Γ, that it imparts on the two components, which is related to the birefringence Δn and the thickness L of the crystal by the formula

The components of a binary star system may be designated by their relative temperatures as the hot companion and cool companion.

The movement of components of a mechanical system is analyzed by attaching a reference frame to each part and determining how the reference frames move relative to each other.

The rigid transformation, or displacement, of M relative to F defines the relative position of the two components.

In the description, only the relative size of the different components matter, and their angle to each other on the complex plane.

The relative presence or absence of these components form the subclasses of dark chocolate, milk chocolate, and white chocolate.

A system was defined as a group of interacting parts and the relative influence of these parts followed rules which, once formulated could be used to describe the system no matter what the actual components were.

The equation of vorticity ( three components in the canonical form ) describes the material derivative ( that is, the local change due to local change with time and advection ) of vorticity, and thus can be stated in either relative or absolute form.

Cartilage is classified in three types, elastic cartilage, hyaline cartilage and fibrocartilage, which differ in the relative amounts of these three main components.

* Separation factor ( alpha ) practically is a relative comparison how well two components of the mixture were separated.