1 Notation and terminology
2 Fields
3 Vector spaces over a field
4 Algebras over a field
5 Linear independence and dimension
6 Linear transformations
7 The endomorphism algebra of a vector space
8 Representation oflinear transformations by matrices
9 The algebra of square matrices
10 Systems of linear equations
11 Determinants
12 Eigenvalues and eigenvectors
13 Krylov subspaces
14 The dual space
15 Inner product spaces

1 Notation and terminology
2 Fields
3 Vector spaces over a field
4 Algebras over a field
5 Linear independence and dimension
6 Linear transformations
7 The endomorphism algebra of a vector space
8 Representation oflinear transformations by matrices
9 The algebra of square matrices
10 Systems of linear equations
11 Determinants
12 Eigenvalues and eigenvectors
13 Krylov subspaces
14 The dual space
15 Inner product spaces
16 Orthogonality
17 Selfadjoint Endomorphisms
18 Unitary and Normal endomorphisms
19 Moore-Penrose pseudoinverses
20 Bilinear transformations and forms
A Summary of Notation
Index