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