matrices

vectors

scalars

matrix transpose

conjugate transpose of

matrix inverse

the inverse of

the inverse of

indicates that is -by-

matrix element of

th row of matrix

th column of matrix

vector dot product

inner product, such as

vector in the th iteration

diag() diagonal of matrix

diag() diagonal matrix constructed from scalars

span() spanning space of vectors

span() , subspace spanned by the columns of

Krylov subspace

matrix whose th column is

entry of

or th column or row of

submatrix consisting of columns 2, 3, and 5 of

submatrix consisting of rows 2, 3, and 5 of

, sets of real and complex numbers

, real and complex -spaces

, vector and matrix -norm

the ``-norm,'' defined as

matrix Frobenius norm

machine precision

eigenvalues of

eigenvalues of with maximum (resp., minimum) modulus

singular values of

largest and smallest singular values of

condition number of matrix , defined as

complex conjugate of the scalar

maximum value in set

minimum value in set

summation

``big-oh'' asymptotic bound

the real part of the complex number

the imaginary part of the complex number

the vector is orthogonal to the vector