Mathematical Notation

Descriptions of LAPACK routines use the following notation:

`Ax = b`	A system of linear equations with an `n`-by-`n` matrix `A = {a_ij}`, a right-hand side vector `b = {b_i}`, and an unknown vector `x = {x_i}`.
`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 `\|x_i\|` (absolute values of `x_i`).
`\|A\|`	the matrix with elements `\|a_ij\|` (absolute values of `a_ij`).
`\|\|x\|\|_∞ = max_i\|x_i\|`	The infinity-norm of the vector `x`.
`\|\|A\|\|_∞ = max_iΣ_j\|a_ij\|`	The infinity-norm of the matrix `A`.
`\|\|A\|\|₁ = max_jΣ_i\|a_ij\|`	The one-norm of the matrix `A`. `\|\|A\|\|₁ = \|\|A^T\|\|_∞ = \|\|A^H\|\|_∞`
`κ(A) = \|\|A\|\| \|\|A^-1\|\|`	The condition number of the matrix `A`.

`Ax = b`	A system of linear equations with an `n`-by-`n` matrix `A = {a_ij}`, a right-hand side vector `b = {b_i}`, and an unknown vector `x = {x_i}`.
`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 `\|x_i\|` (absolute values of `x_i`).
`\|A\|`	the matrix with elements `\|a_ij\|` (absolute values of `a_ij`).
`\|\|x\|\|_∞ = max_i\|x_i\|`	The infinity-norm of the vector `x`.
`\|\|A\|\|_∞ = max_iΣ_j\|a_ij\|`	The infinity-norm of the matrix `A`.
`\|\|A\|\|₁ = max_jΣ_i\|a_ij\|`	The one-norm of the matrix `A`. `\|\|A\|\|₁ = \|\|A^T\|\|_∞ = \|\|A^H\|\|_∞`
`κ(A) = \|\|A\|\| \|\|A^-1\|\|`	The condition number of the matrix `A`.