# Mathematical Notation

In addition to the mathematical notation used in previous chapters, descriptions of routines in this chapter use the following notation:

λi

  Eigenvalues of the matrix A (for the definition of eigenvalues, see Eigenvalue Problems).

σi

  Singular values of the matrix A. They are equal to square roots of the eigenvalues of AHA. (For more information, see Singular Value Decomposition).

`||x||2`

  The 2-norm of the vector x: `||x||2 = (Σi|xi|2)1/2 = ||x||E` .

`||A||2`

  The 2-norm (or spectral norm) of the matrix A.

  `||A||2 = maxiσi`, `||A||22= max|x|=1(Ax·Ax)`.

`||A||E`

  The Euclidean norm of the matrix A: `||A||E2 = ΣiΣj|aij|2` (for vectors, the Euclidean norm and the 2-norm are equal: `||x||E = ||x||2)`.

`q(x, y)`

  The acute angle between vectors x and y:

  `cos q(x, y) = |x·y| / (||x||2||y||2)`.

Parent topic: LAPACK Routines: Least Squares and Eigenvalue Problems