# Mathematical Notation

Descriptions of LAPACK routines use the following notation:

`Ax = b` | A system of linear equations with an n-by-n matrix `A = {aij}`, a right-hand side vector `b = {bi}`, and an unknown vector `x = {xi}`.
`AX = B` | A set of systems with a common matrix A and multiple right-hand sides. The columns of B are individual right-hand sides, and the columns of X are the corresponding solutions.
`|x|` | the vector with elements `|xi|` (absolute values of `xi`).
`|A|` | the matrix with elements `|aij|` (absolute values of `aij`).
`||x||∞ = maxi|xi|` | The infinity-norm of the vector x.
`||A||∞ = maxiΣj|aij|` | The infinity-norm of the matrix A.
`||A||1 = maxjΣi|aij|` | The one-norm of the matrix A. `||A||1 = ||AT||∞ = ||AH||∞`
`κ(A) = ||A|| ||A-1||` | The condition number of the matrix A.

Parent topic: LAPACK Routines: Linear Equations