# Symbols:Vector Algebra

## Symbols used in Vector Algebra

### 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 $\mathbf x \times \mathbf y$ is \mathbf x \times \mathbf y .

### 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 $\mathbf x \cdot \mathbf y$ is \mathbf x \cdot \mathbf y .

### Del Operator

$\nabla$

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

Let $\tuple {\mathbf e_1, \mathbf e_2, \ldots, \mathbf e_n}$ be the standard ordered basis of $\mathbf V$.

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

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

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

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

## Deprecated Symbols

This page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.

However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ the intention is to present a consistent style, and so these symbols are to be considered deprecated.

### Cross Product

$\wedge$

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 .