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 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.
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.
Orthogonal diagonalizationIn linear algebra, an orthogonal diagonalization of a symmetric matrix is a diagonalization by means of an orthogonal change of coordinates. The following is an orthogonal diagonalization algorithm that diagonalizes a quadratic form q(x) on Rn by means of an orthogonal change of coordinates X = PY. Step 1: find the symmetric matrix A which represents q and find its characteristic polynomial Step 2: find the eigenvalues of A which are the roots of . Step 3: for each eigenvalue of A from step 2, find an orthogonal basis of its eigenspace.
FlowerA flower, sometimes known as a bloom or blossom, is the reproductive structure found in flowering plants (plants of the division Angiospermae). Flowers produce gametophytes, which in flowering plants consist of a few haploid cells which produce gametes. The "male" gametophyte, which produces non-motile sperm, is enclosed within pollen grains; the "female" gametophyte is contained within the ovule. When pollen from the anther of a flower is deposited on the stigma, this is called pollination.
GenerationA generation refers to all of the people born and living at about the same time, regarded collectively. It can also be described as, "the average period, generally considered to be about 20–30 years, during which children are born and grow up, become adults, and begin to have children." In kinship terminology, it is a structural term designating the parent-child relationship. It is known as biogenesis, reproduction, or procreation in the biological sciences.
Language of flowersFloriography (language of flowers) is a means of cryptological communication through the use or arrangement of flowers. Meaning has been attributed to flowers for thousands of years, and some form of floriography has been practiced in traditional cultures throughout Europe, Asia, and Africa. Plants and flowers are used as symbols in the Hebrew Bible, particularly of love and lovers in the Song of Songs, as an emblem for the Israelite people, and for the coming Messiah.
Socialist calculation debateThe socialist calculation debate, sometimes known as the economic calculation debate, was a discourse on the subject of how a socialist economy would perform economic calculation given the absence of the law of value, money, financial prices for capital goods and private ownership of the means of production. More specifically, the debate was centered on the application of economic planning for the allocation of the means of production as a substitute for capital markets and whether or not such an arrangement would be superior to capitalism in terms of efficiency and productivity.
GenotypeThe genotype of an organism is its complete set of genetic material. Genotype can also be used to refer to the alleles or variants an individual carries in a particular gene or genetic location. The number of alleles an individual can have in a specific gene depends on the number of copies of each chromosome found in that species, also referred to as ploidy. In diploid species like humans, two full sets of chromosomes are present, meaning each individual has two alleles for any given gene.
Calculation in kindNOTOC Calculation in kind or calculation in-natura is a way of valuating resources and a system of accounting that uses disaggregated physical magnitudes as opposed to a common unit of calculation. As the basis for a socialist economy, it was proposed to replace money and financial calculation. In an in-kind economy products are produced for their use values (their utility) and accounted in physical terms. By contrast, in money-based economies, commodities are produced for their exchange value and accounted in monetary terms.
Singular valueIn mathematics, in particular functional analysis, the singular values, or s-numbers of a compact operator acting between Hilbert spaces and , are the square roots of the (necessarily non-negative) eigenvalues of the self-adjoint operator (where denotes the adjoint of ). The singular values are non-negative real numbers, usually listed in decreasing order (σ1(T), σ2(T), ...). The largest singular value σ1(T) is equal to the operator norm of T (see Min-max theorem).
Cut flowersCut flowers are flowers and flower buds (often with some stem and leaf) that have been cut from the plant bearing it. It is removed from the plant for decorative use. Cut greens are leaves with or without stems added to the cut flowers for contrast and design purposes. These displays improve the quality of the human environment. Floral design professionals work at florist shops (floristry) and use their design skills and experience with many types of flowers and greens to create works of art with flowers.
