# Symbols:Vector Algebra

## Vector Cross Product

$\times$

$\mathbf x \times \mathbf y$ means the cross product of $\mathbf x$ and $\mathbf y$, a binary operation on two vectors of a $3$-dimensional vector space which produces another such vector.

The $\LaTeX$ code for $\times$ is \times .

See Set Operations and Relations and Arithmetic and Algebra for alternative definitions of this symbol.

## Vector Scalar Product

$\cdot$

$\mathbf x \cdot \mathbf y$ means the dot product of $\mathbf x$ and $\mathbf y$, a binary operation on two vectors which produces a scalar.

The $\LaTeX$ code for $\cdot$ is \cdot .

See Arithmetic and Algebra, Group Theory and Logical Operators: Deprecated Symbols for alternative definitions of this symbol.

## Del Operator

$\nabla$

Let $\mathbf V$ be a vector space of $n$ dimensions.

Let $\left({\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}\right)$ be the standard ordered basis of $\mathbf V$.

The del operator is a unary operator on $\mathbf V$ defined as:

$\nabla := \displaystyle \sum_{k \mathop = 1}^n \mathbf e_k \dfrac \partial {\partial x_k}$

where $\mathbf v = \displaystyle \sum_{k \mathop = 0}^n x_k \mathbf e_k$ is an arbitrary vector of $\mathbf V$.

The $\LaTeX$ code for $\nabla$ is \nabla .

## Deprecated Symbols

$\wedge$

Some authors use $\mathbf A \wedge \mathbf B$ to mean $\mathbf A \times \mathbf B$, that is, the vector cross product.

The $\LaTeX$ code for $\wedge$ is \wedge .

The same symbol can be produced using \land, but this is usually used when the symbol is used in the sense of the logical and context.

See Logical Operators and Group Theory for alternative definitions of this symbol.