# Vector Calculus Notation

Mathematical notation is designed to create the correct ideas in the mind of the reader. It is deliberately ambiguous and incomplete; indeed, it is almost meaningless to all other readers.
-- Poppelier, Herwijnen and Rowley, "Standard dtd's and scientific publishing"

As the following table demonstrates, the notations used in vector calculus are myriad. Indeed, this table is not exhaustive.

For the sake of uniformity, these pages will in general use bold letters for vectors and unit vectors, such as v for a vector and i for a unit vector.
Symbol Definition N-tuple of real numbers Space of all N-tuples Component-wise N-tuple addition Scalar multiplication of an N-tuple The origin the line segment between P and Q the line through P and Q A vector variable The zero vector The magnitude of a vector variable Displacement vector from P1 to P2 Unit vector in the direction of the positive x-axis Unit vector in the direction of the positive y-axis Unit vector in the direction of the positive z-axis Vector addition Vector negatition Scalar multiplication of a vector Geometric definition of dot product Algebraic definition of dot product (N=3) Cross product Distance from z-axis in cylindrical coordinates

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Last modified November 14, 1998