# Vertex operator algebra

May 29th, 2015
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In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely

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vectorsDefinition of VectorA vector is a quantity with a magnitude and a direction, represented by an arrow.A vector has head A and tail B, represented as , or as a lowercase letter ,.Do not think of vector has a segment with a fixed place. It is actually embedded throughout the coordinate plane.2 vectors are equal if their magnitudes and directions are equal.A zero vector has no magnitude; it starts and ends at A.Adding and Subtracting VectorsGiven 2 vectors, and , draw and . Vector is called the sum of vectors and . Paralellogram ruleIf ABCD is a parallelogram, then .Properties of Vector AdditionIf are vectors, then: (Commutative Property)( (Associative Property) (Identity Property of Addition) Difference of 2 Vectors is the vector with the same magnitude but opposite direction with .Given 2 vectors and , the difference of and is vector , notated as .Given 3 points A, B, C, we have .Multiplying a Vector with a ScalarGiven real number k ? 0 and vector ? 0. The product of k and is notated and has the same direction with if k > 0 and has the opposite direction with if k < 0, and has magnitude We define 0.Properties of Multiplying a Vector with a

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