Algebra1. the abstract study of number systems and operations within them, including such advanced topics as groups, rings, invariant theory, and cohomology. = abstract algebra 2. a particular type of algebraic structure. Formally, an algebra is a vector space V over a field F with a multiplication, which is distributive, and for every f from F and every x,y from V
Etymology: from the title of a work written around 825 by the Arabic mathematician known as al-Khowarizmi, entitled al-jebr w' al-muqabalah. In Arabic, al- is the definite article "the." The first noun [Schwartzman, S. (2012). The Words of Mathematics: An Etymological Dictionary of Mathematical Terms used in English. Washington: The Mathematical Association of America.] | |
annihilatornoun Pronunciation: /ɐnˈaɪ.ə.leɪtə/ Definition: Let M be a left modul over a ring R and let S be a subset of M. The annihilator of S is the set of all r from R such that sr is equal to zero (for all s from S). Source: |
Associativitynoun Pronunciation: [ə,səʊsɪə'tɪvɪti] Meaning: a property of a binary operation; if it holds, then with more than one of the same operator, the order of operations does not matter Example: if + is an associative operator, then for every three elements a, b, c it holds that a + (b + c) = (a + b) + c Source: |
BasisNoun The figure shows the basis vectors i,j, k, and the vector a is a linear combination of them.
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BijectionNoun
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CommutativityNoun Etymology |
Construction/kənˈstrʌk.ʃən/ A finite sequence of steps. The steps are defined by author of the task, classical example is Eucleidian construction by straightedge and compass. |
Coprime (integers)Adjective
Antonym Etymology |
DeterminantNoun Pronunciation |
DimensionDimension, n. Pronounciation: /dɪˈmɛnʃən/ Meaning: 1) Geometry. A mode of linear measurement, magnitude, or extension, in a particular direction; usually as co-existing with similar measurements or extensions in other directions. 2) Algebra. Since the product of two, or of three, quantities, each denoting a length (i.e. a magnitude of one dimension), represents an area or a volume (i.e. a magnitude of two, or of three, dimensions), such products themselves are said to be of so many dimensions; and generally, the number of dimensions of a product is the number of the (unknown or variable) quantities contained in it as factors (known or constant quantities being reckoned of no dimensions); any power of a quantity being of the dimensions denoted by its index. Source: |