Symbols:Vector Algebra

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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:

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

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

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page contains symbols which may or may not be in current use, but are either non-standard in mathematics or have been superseded by their more modern variants.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