All the beautiful mathematical ideas can be found in Numerical Linear Algebra. However, the subject is better to be enjoyed by researchers than to teach to students as many excellent ideas are often buried in the complicated notation. A researcher must be aware of this fact.

Gene H. Golub . Lecture at University of Liverpool (1995)

Throughout the book, capital letters such as A denote a rectangular matrix m n (or a square matrix of size n), whose ( i, j) entry is denoted by A( i, j) = a _ij, and small letters such as x, b denote vectors of size n unless stated otherwise i.e. A ? ^{m n} and x, b ? ⁿ.

Some (common) abbreviations and notations are listed here

• ? the space of all complex vectors of size n

• ⁿ ? the space of all real vectors of size n [note ⁿ ? and ^{n n} ? ^{n n} )]

• A ? A norm of matrix A (see 1.5)

• A ? The matrix of absolute values of A i.e. ( A) _ij = A( i, j)= a _ij.

• A ^T ?The transpose of A i.e. A ^T ( i, j)= A( j, i). [ A is symmetric if A ^T = A]