Each C *- algebra, Ae, is isomorphic ( in a noncanonical way ) to the full matrix algebra M < sub > dim ( e )</ sub >( C ).

Each interpretation is responsible for different distributive laws in the Boolean algebra.

Each algebra consists of linear combinations ( with complex coefficients ) of two basis elements, 1 ( the identity element ) and a.

Each Lie algebra has an associated Lie group and a Lie superalgebra can sometimes be extended into representations of a Lie supergroup.

Each Boolean algebra is mapped to a specific topology on the set of ultrafilters of.

* Relational algebra: Each row or record in the above table meets the standard definition of a tuple under relational algebra ( the above example depicts a series of 3-tuples ).

Each Boolean algebra B has an associated topological space, denoted here S ( B ), called its Stone space.

Each congruence on A is a subalgebra of the product algebra AxA, so Con ( A ) ⊆ Sub ( AxA ).

Each of these methods involves the application of a construction from linear algebra to representation theory.

Each contest contains 6 short-answer questions to solve in 30 minutes, covering geometry, algebra, trigonometry, and other advanced pre-calculus topics.

the algebra for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space as follows: Each is identified with the multiplication operator

Each trial consists of choosing a student manager at random.

Each round consists of several processing steps, including one that depends on the encryption key itself.

Each chipset consists of several coprocessors which handle graphics acceleration, digital audio, direct memory access and communication between various peripherals ( e. g., CPU, memory and floppy disks ).

Each set consists of nine ends and the player with the most shots at the end of a set wins the set.

Each team consists of a maximum of 11 players ( excluding substitutes ), one of whom must be the goalkeeper.

Each hour consists of headlines on each quarter hour, extended at the top of the hour to form the main part of the daily schedule though these are interspaced with other programmes, generally at weekends.

Each Upper House consists of three floors.

Each half-cell consists of an electrode, and an electrolyte.

Each homotopy class consists of all loops which wind around the circle a given number of times ( which can be positive or negative, depending on the direction of winding ).

Each codon consists of three nucleotide s, usually representing a single amino acid.

Each team consists of 7 players on court and 7 substitute players on the bench.

Each branch of the hyperbola consists of two arms which become straighter ( lower curvature ) further out from the center of the hyperbola.

That is, although the syllable 한 han may look like a single character, it is composed of three letters: ㅎ h, ㅏ a, and ㄴ n. Each syllabic block consists of two to five letters, including at least one consonant and one vowel.

Each stage consists of a specialized form of warfare and its associated tactics.

Each pixel of an LCD typically consists of a layer of molecules aligned between two transparent electrodes, and two polarizing filters, the axes of transmission of which are ( in most of the cases ) perpendicular to each other.

Each daughter cell now has half the number of chromosomes but each chromosome consists of a pair of chromatids.

Each part consists of its own content header ( zero or more Content-header fields ) and a body.

Each tetrachord consists of two whole steps followed by a half step.

Each metabolic pathway consists of a series of biochemical reactions that are connected by their intermediates: the products of one reaction are the substrates for subsequent reactions, and so on.

Each nucleotide consists of three components: a purine or pyrimidine nucleobase ( sometimes termed nitrogenous base or simply base ), a pentose sugar, and a phosphate group.

Each atomic nucleus consists of one or more nucleons, and each atom in turn consists of a cluster of nucleons surrounded by one or more electrons.

Each term consists of the product of a constant ( called the coefficient of the term ) and a finite number of variables ( usually represented by letters ), also called indeterminates, raised to whole number powers.

Each of the 12 pentacubes consists of 5 unit cubes, and are like 2D pentominoes but with unit thickness.

Each team consists of four mounted players, which can be mixed teams of both men and women.

Each observable is represented by a maximally Hermitian ( precisely: by a self-adjoint ) linear operator acting on the state space.

) Each column of is a linear combination of the columns of.

Each bulb generally produces just two or three linear leaves and an erect, leafless scape ( flowering stalk ), which bears at the top a pair of bract-like spathe valves joined by a papery membrane.

Each protein exists as an unfolded polypeptide or random coil when translated from a sequence of mRNA to a linear chain of amino acids.

Each antenna element consists of a crossed dipole that can be polarized for linear, ordinary mode ( O-mode ), or extraordinary mode ( X-mode ) transmission and reception.

Each segment begins at a multiple of 16 bytes, from the beginning of the linear ( flat ) address space.

Each protein exists as an unfolded polypeptide or random coil when translated from a sequence of mRNA to a linear chain of amino acids.

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

Each mission is structured through a number of linear levels, each with differing locations, levels of action and styles of gameplay.

These are ten in number ; therefore the cubic curves form a projective space of dimension 9, over any given field K. Each point P imposes a single linear condition on F, if we ask that C pass through P. Therefore we can find some cubic curve through any nine given points, which may be degenerate, and may not be unique, but will be unique and non-degenerate if the points are in general position ; compare to two points determining a line and how five points determine a conic.

Each battleground is a linear path in which the player's base is located on one side and the enemy base is located on the other side.

Each two-photon polarization state can be expressed as a linear combination of these four basis states with complex coefficients.

Each of these genomes forms a chromosome with a linear structure, unlike most bacterial genomes, which exist in the form of circular chromosomes.

Each RMC consist of two sets of widely-spaced, fine-scale linear grids.

The first stage consists of searching for a set of r linearly independent relations between the factor base and power of the generator g. Each relation contributes one equation to a system of linear equations in r unknowns, namely the discrete logarithms of the r primes in the factor base.

Each leaflet is linear to lanceolate or oblong-obovate, 8 – 25 cm long and 0. 5 – 2 cm broad, with distinct teeth at the tip.

Each leaflet is linear to lanceolate or oblong-obovate, 8-25 cm long and 0. 5-2 cm broad, entire or with indistinct teeth at the tip.

Each group of light consists of three sequential flashing lights in linear configuration.

Each point on a given facet will satisfy the linear equality of the corresponding row in the matrix.

Each summary block contains a pointer to the next summary block, linking segments into one long chain that LFS treats as a linear log.

In this process, a d-dimensional spacetime is considered as formed by space slices that are labeled by a discrete time variable t. Each space slice is approximated by a simplicial manifold composed by regular ( d-1 )- dimensional simplices and the connection between these slices is made by a piecewise linear manifold of d-simplices.