Pensumliste for MAT-1004 Lineær algebra, våren 2008

Lærebok:
H. Anton and C.Rorres, "Elementary Linear Algebra. Applications version", 9. ed.

Pensum:
(Godkjent av instituttstyret 12.02.04)

Chapter 1 Systems of Linear Equations and Matrices (73 sider)
1.1 Introduction to Systems of Linear Equations
1.2 Gaussian Elimination
1.3 Matrices and Matrix Operations
1.4 Inverses; Rules of Matrix Arithmetic
1.5 Elementary Matrices and a Method for Finding A-1
1.6 Futher Results on Systems of Equations and Invertibility
1.7 Diagonal, Triangular, and Symmetric Matrices

Chapter 2 Determinants (32 sider)
2.1 The Determinant Function
2.2 Evaluating Determinants by Row Reduction
2.3 Properties of the Determinant Function
2.4 Cofactor Expansion; Cramer's Rule

Chapter 3 Vector in 2-Space and 3-Space (39 sider)
3.1 Introduction to Vectors (geometric)
3.2 Norm of a Vector; Vector Arithmetic
3.3 Dot Product; Projections
3.4 Cross Product
3.5 Lines and Planes in 3-Space

Chapter 4 Euclidean Vector Spaces (36 sider)
4.1 Euclidean n-Space
4.2 Linear Transformations from Rn to Rm
4.3 Properties of Linear Transformations from Rn to Rm

Chapter 5 General Vector Spaces (67 sider)
5.1 Real Vector Spaces
5.2 Subspaces
5.3 Linear Independence
5.4 Basis and Dimension
5.5 Row Space, Column Space, and Nullspace
5.6 Rank and Nullity

Chapter 6 (10 sider)
6.5. Change of basis
6.6. Orthogonal matrices

Chapter 7 Eigenvalues, Eigenvectors (23 sider)
7.1 Eigenvalues and Eigenvectors
7.2 Diagonalization
7.3 Orthogonal Diagonalization + Kompendiet.

Chapter 8 Linear Transformations (47 sider)
8.1 General Linear Transformations
8.2 Kernel and Range
8.3 Inverse Linear Transformations
8.4 Matrices of general Linear Transformations
8.5 Similarity


Til sammen: 327 sider

Adgang til eksamen og tillatte hjelpemidler:
Rottmanns tabeller
Godkjente statistiske tabeller
To A4-ark (4 sider) med egne notater
Godkjent kalkulator, se liste.