Table of Contents
Notation and conventions used on this site
Every textbook, website, professor, etc. uses their own notation and conventions. To avoid confusion I thought I'd write down mine and try to use them consistently throughout the site.
|The norm of the vector (a scalar), if it appears in the text. Otherwise, it's some scalar.|
|The inner product of a vector with itself (a scalar). Equivalently, the norm of the vector squared.|
|The norm of a vector expression (a scalar).|
|The inner product of two vectors (a scalar).|
|The cross product of two vectors (a vector).|
|A matrix product (a matrix). The former is premultiplying the latter or, equivalently, the latter is postmultiplying the former.|
|A matrix premultiplying a vector or, equivalently, operating on it (a vector).|
|The Kronecker product of two matrices (a matrix).|
|The inverse of an invertible square matrix (a matrix).|
|The determinant of a square matrix (a scalar).|
|The trace of a square matrix (a scalar).|
Generally I avoid using indices because of the inherent complexity associated with coordinates. When I do, though, I try to be consistent with Ricci calculus. Below is a quick summary:
|A superscript.||A contravariant index.|
|A subscript.||A covariant index.|
|| The i-th coordinate of a vector (which transforms contravariantly).
I use round brackets to avoid confusion if necessary (in which case the index appears outside).
|The i-th coordinate of a covector (which transforms covariantly).|
| An element of a (1,1)-tensor.
When the tensor is treated as a linear transformation, this is the element of the corresponding matrix that lies at the intersection of the i-th row and the j-th column.
If and are undefined then this denotes the entire tensor.
|A vector field. These usually have uppercase symbols.|
|The gradient of a scalar field (a vector field).|
|The divergence of a vector field (a scalar field).|
|The curl of a vector field (a vector field).|
|The Laplacian of a scalar field (a scalar field).|