Matrix multiplicationIn mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
CapillaryA capillary is a small blood vessel, from 5 to 10 micrometres in diameter, and is part of the microcirculation system. Capillaries are microvessels and the smallest blood vessels in the body. They are composed of only the tunica intima (the innermost layer of an artery or vein), consisting of a thin wall of simple squamous endothelial cells. They are the site of the exchange of many substances from the surrounding interstitial fluid, and they convey blood from the smallest branches of the arteries (arterioles) to those of the veins (venules).
Lymph capillaryLymph capillaries or lymphatic capillaries are tiny, thin-walled microvessels located in the spaces between cells (except in the central nervous system and non-vascular tissues) which serve to drain and process extracellular fluid. Upon entering the lumen of a lymphatic capillary, the collected fluid is known as lymph. Each lymphatic capillary carries lymph into a lymphatic vessel, which in turn connects to a lymph node, a small bean-shaped gland that filters and monitors the lymphatic fluid for infections.
LymphLymph (from Latin, lympha, meaning "water") is the fluid that flows through the lymphatic system, a system composed of lymph vessels (channels) and intervening lymph nodes whose function, like the venous system, is to return fluid from the tissues to be recirculated. At the origin of the fluid-return process, interstitial fluid—the fluid between the cells in all body tissues—enters the lymph capillaries.
Invertible matrixIn linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.
CollagenCollagen (ˈkɒlədʒən) is the main structural protein in the extracellular matrix found in the body's various connective tissues. As the main component of connective tissue, it is the most abundant protein in mammals, making up from 25% to 35% of the whole-body protein content. Collagen consists of amino acids bound together to form a triple helix of elongated fibril known as a collagen helix. It is mostly found in connective tissue such as cartilage, bones, tendons, ligaments, and skin.
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
FibrinFibrin (also called Factor Ia) is a fibrous, non-globular protein involved in the clotting of blood. It is formed by the action of the protease thrombin on fibrinogen, which causes it to polymerize. The polymerized fibrin, together with platelets, forms a hemostatic plug or clot over a wound site. When the lining of a blood vessel is broken, platelets are attracted, forming a platelet plug. These platelets have thrombin receptors on their surfaces that bind serum thrombin molecules, which in turn convert soluble fibrinogen in the serum into fibrin at the wound site.
Extracellular fluidIn cell biology, extracellular fluid (ECF) denotes all body fluid outside the cells of any multicellular organism. Total body water in healthy adults is about 60% (range 45 to 75%) of total body weight; women and the obese typically have a lower percentage than lean men. Extracellular fluid makes up about one-third of body fluid, the remaining two-thirds is intracellular fluid within cells. The main component of the extracellular fluid is the interstitial fluid that surrounds cells.
Vascular endothelial growth factorVascular endothelial growth factor (VEGF, vɛdʒ'ɛf), originally known as vascular permeability factor (VPF), is a signal protein produced by many cells that stimulates the formation of blood vessels. To be specific, VEGF is a sub-family of growth factors, the platelet-derived growth factor family of cystine-knot growth factors. They are important signaling proteins involved in both vasculogenesis (the de novo formation of the embryonic circulatory system) and angiogenesis (the growth of blood vessels from pre-existing vasculature).
CoagulationCoagulation, also known as clotting, is the process by which blood changes from a liquid to a gel, forming a blood clot. It potentially results in hemostasis, the cessation of blood loss from a damaged vessel, followed by repair. The mechanism of coagulation involves activation, adhesion and aggregation of platelets, as well as deposition and maturation of fibrin. Coagulation begins almost instantly after an injury to the endothelium lining a blood vessel.
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Tissue engineeringTissue engineering is a biomedical engineering discipline that uses a combination of cells, engineering, materials methods, and suitable biochemical and physicochemical factors to restore, maintain, improve, or replace different types of biological tissues. Tissue engineering often involves the use of cells placed on tissue scaffolds in the formation of new viable tissue for a medical purpose but is not limited to applications involving cells and tissue scaffolds.
AngiogenesisAngiogenesis is the physiological process through which new blood vessels form from pre-existing vessels, formed in the earlier stage of vasculogenesis. Angiogenesis continues the growth of the vasculature mainly by processes of sprouting and splitting, but processes such as coalescent angiogenesis, vessel elongation and vessel cooption also play a role. Vasculogenesis is the embryonic formation of endothelial cells from mesoderm cell precursors, and from neovascularization, although discussions are not always precise (especially in older texts).
EndotheliumThe endothelium (: endothelia) is a single layer of squamous endothelial cells that line the interior surface of blood vessels and lymphatic vessels. The endothelium forms an interface between circulating blood or lymph in the lumen and the rest of the vessel wall. Endothelial cells form the barrier between vessels and tissue and control the flow of substances and fluid into and out of a tissue. Endothelial cells in direct contact with blood are called vascular endothelial cells whereas those in direct contact with lymph are known as lymphatic endothelial cells.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Endothelial progenitor cellEndothelial progenitor cell (or EPC) is a term that has been applied to multiple different cell types that play roles in the regeneration of the endothelial lining of blood vessels. Outgrowth endothelial cells are an EPC subtype committed to endothelial cell formation. Despite the history and controversy, the EPC in all its forms remains a promising target of regenerative medicine research. Developmentally, the endothelium arises in close contact with the hematopoietic system.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Function compositionIn mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x.
