Search results
Results from the WOW.Com Content Network
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time. [ 1 ] Specific types of mathematical diagrams
In mathematics, a diagram algebra is an algebraic structure in which operations are performed using diagrams rather than traditional techniques. In particular ...
A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 [ 1 ] [ 2 ] as a refinement of Edward W. Veitch 's 1952 Veitch chart , [ 3 ] [ 4 ] which itself was a rediscovery of Allan Marquand 's 1881 logical diagram [ 5 ] [ 6 ] or Marquand diagram . [ 4 ]
In abstract algebra, an automorphism of a Lie algebra is an isomorphism from to itself, that is, a bijective linear map preserving the Lie bracket. The set of automorphisms of g {\displaystyle {\mathfrak {g}}} are denoted Aut ( g ) {\displaystyle {\text{Aut}}({\mathfrak {g}})} , the automorphism group of g {\displaystyle {\mathfrak {g}}} .
The matrix P represents the weather model in which a sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. [4] The columns can be labelled "sunny" and "rainy", and the rows can be labelled in the same order. The above matrix as a graph.
The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. [1] Its subalgebras include diagram algebras such as the Brauer algebra, the Temperley–Lieb algebra, or the group algebra of the symmetric group. Representations of the partition algebra are built from sets ...
A finite-dimensional simple complex Lie algebra is isomorphic to either of the following: , , (classical Lie algebras) or one of the five exceptional Lie algebras. [1]To each finite-dimensional complex semisimple Lie algebra, there exists a corresponding diagram (called the Dynkin diagram) where the nodes denote the simple roots, the nodes are jointed (or not jointed) by a number of lines ...