Eigenvalues and eigenvectorsIn linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.
HeartThe heart is a muscular organ in most animals. This organ pumps blood through the blood vessels of the circulatory system. The pumped blood carries oxygen and nutrients to the body, while carrying metabolic waste such as carbon dioxide to the lungs. In humans, the heart is approximately the size of a closed fist and is located between the lungs, in the middle compartment of the chest, called the mediastinum. In humans, other mammals, and birds, the heart is divided into four chambers: upper left and right atria and lower left and right ventricles.
Heart rateHeart rate (or pulse rate) is the frequency of the heartbeat measured by the number of contractions of the heart per minute (beats per minute, or bpm). The heart rate can vary according to the body's physical needs, including the need to absorb oxygen and excrete carbon dioxide, but is also modulated by numerous factors, including (but not limited to) genetics, physical fitness, stress or psychological status, diet, drugs, hormonal status, environment, and disease/illness as well as the interaction between and among these factors.
Artificial heart valveAn artificial heart valve is a one-way valve implanted into a person's heart to replace a heart valve that is not functioning properly (valvular heart disease). Artificial heart valves can be separated into three broad classes: mechanical heart valves, bioprosthetic tissue valves and engineered tissue valves. The human heart contains four valves: tricuspid valve, pulmonary valve, mitral valve and aortic valve. Their main purpose is to keep blood flowing in the proper direction through the heart, and from the heart into the major blood vessels connected to it (the pulmonary artery and the aorta).
Heart valveA heart valve is a one-way valve that allows blood to flow in one direction through the chambers of the heart. Four valves are usually present in a mammalian heart and together they determine the pathway of blood flow through the heart. A heart valve opens or closes according to differential blood pressure on each side. The four valves in the mammalian heart are two atrioventricular valves separating the upper atria from the lower ventricles – the mitral valve in the left heart, and the tricuspid valve in the right heart.
Eigendecomposition of a matrixIn linear algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Only diagonalizable matrices can be factorized in this way. When the matrix being factorized is a normal or real symmetric matrix, the decomposition is called "spectral decomposition", derived from the spectral theorem. Eigenvalue, eigenvector and eigenspace A (nonzero) vector v of dimension N is an eigenvector of a square N × N matrix A if it satisfies a linear equation of the form for some scalar λ.
Congenital heart defectA congenital heart defect (CHD), also known as a congenital heart anomaly, congenital cardiovascular malformation, and congenital heart disease, is a defect in the structure of the heart or great vessels that is present at birth. A congenital heart defect is classed as a cardiovascular disease. Signs and symptoms depend on the specific type of defect. Symptoms can vary from none to life-threatening. When present, symptoms are variable and may include rapid breathing, bluish skin (cyanosis), poor weight gain, and feeling tired.
KryptonKrypton (from κρυπτός 'the hidden one') is a chemical element with the symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace amounts in the atmosphere and is often used with other rare gases in fluorescent lamps. Krypton is chemically inert. Krypton, like the other noble gases, is used in lighting and photography. Krypton light has many spectral lines, and krypton plasma is useful in bright, high-powered gas lasers (krypton ion and excimer lasers), each of which resonates and amplifies a single spectral line.
Period 5 elementA period 5 element is one of the chemical elements in the fifth row (or period) of the periodic table of the chemical elements. The periodic table is laid out in rows to illustrate recurring (periodic) trends in the chemical behaviour of the elements as their atomic number increases: a new row is begun when chemical behaviour begins to repeat, meaning that elements with similar behaviour fall into the same vertical columns. The fifth period contains 18 elements, beginning with rubidium and ending with xenon.
Period 4 elementA period 4 element is one of the chemical elements in the fourth row (or period) of the periodic table of the chemical elements. The periodic table is laid out in rows to illustrate recurring (periodic) trends in the chemical behaviour of the elements as their atomic number increases: a new row is begun when chemical behaviour begins to repeat, meaning that elements with similar behaviour fall into the same vertical columns. The fourth period contains 18 elements beginning with potassium and ending with krypton – one element for each of the eighteen groups.
Generalized eigenvectorIn linear algebra, a generalized eigenvector of an matrix is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector. Let be an -dimensional vector space and let be the matrix representation of a linear map from to with respect to some ordered basis. There may not always exist a full set of linearly independent eigenvectors of that form a complete basis for . That is, the matrix may not be diagonalizable.
Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Transition metalIn chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be transition metals as well. Since they are metals, they are lustrous and have good electrical and thermal conductivity.
Krypton difluorideKrypton difluoride, KrF2 is a chemical compound of krypton and fluorine. It was the first compound of krypton discovered. It is a volatile, colourless solid at room temperature. The structure of the KrF2 molecule is linear, with Kr−F distances of 188.9 pm. It reacts with strong Lewis acids to form salts of the KrF+ and KrF3+ cations. The atomization energy of KrF2 (KrF2(g) → Kr(g) + F2(g)) is 21.9 kcal/mol, giving an average Kr–F bond energy of only 11 kcal/mol, the weakest of any isolable fluoride.
Eigenvalue algorithmIn numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue algorithms may also find eigenvectors. Eigenvalues and eigenvectors and Generalized eigenvector Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.
Energy policyEnergy policy is the manner in which a given entity (often governmental) has decided to address issues of energy development including energy conversion, distribution and use as well as reduction of greenhouse gas emissions in order to contribute to climate change mitigation. The attributes of energy policy may include legislation, international treaties, incentives to investment, guidelines for energy conservation, taxation and other public policy techniques. Energy is a core component of modern economies.
Defective matrixIn linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.
Energy developmentEnergy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include the production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reuse of energy that would otherwise be wasted. Energy conservation and efficiency measures reduce the demand for energy development, and can have benefits to society with improvements to environmental issues.
Zintl phaseIn chemistry, a Zintl phase is a product of a reaction between a group 1 (alkali metal) or group 2 (alkaline earth metal) and main group metal or metalloid (from groups 13, 14, 15, or 16). It is characterized by intermediate metallic/ionic bonding. Zintl phases are a subgroup of brittle, high-melting intermetallic compounds that are diamagnetic or exhibit temperature-independent paramagnetism and are poor conductors or semiconductors. This type of solid is named after German chemist Eduard Zintl who investigated them in the 1930s.
MetalloidA metalloid is a type of chemical element which has a preponderance of properties in between, or that are a mixture of, those of metals and nonmetals. There is no standard definition of a metalloid and no complete agreement on which elements are metalloids. Despite the lack of specificity, the term remains in use in the literature of chemistry. The six commonly recognised metalloids are boron, silicon, germanium, arsenic, antimony and tellurium. Five elements are less frequently so classified: carbon, aluminium, selenium, polonium and astatine.
