Ch. 1: Introduction (first glimpses on Gaussian
elimination)
Intersecting lines in the plane and
the Gauss-Jordan process (uudistettava)
Ch. 2: Linear systems
Visualization of three planes in 3-space
(Maple worksheet)
Planes in 3-space and the Gauss-Jordan
reduction (also links to Maple worksheets)
Solutions in vector form (to be done)
Ch. 3: Matrix algebra
Matrix algebra using Maple (to be done)
Visualization of Example 4.2.1 (Maple
worksheet)
Visualization of Problem 4.1.2 (Maple
worksheet)
Visualization of Problem 4.1.3 (Maple
worksheet)
Visualization of Problem 4.2.3 (Maple
worksheet)
Ch. 4: Analytic geometry
Suora vektorimuodossa
(versio 1) kesken
Ch. 6: Determinants
Vector approach to determinants
(pdf-document by Lehman)
Vectors
and determinants, unit and signed area (JSXgraph)
Ch. 9: Linear space (JSXgraph)
Internal binary
operations in R
Real scalings in R
Linear structure
in R2
Meaning of the Axioms
Operations on intervals
Translated operations
on a line U in the plane
Translated operations
in the plane
Linear space over complex numbers - dimension? (to be done)
Ch 10. Subspaces (JSXgraph)
Tason aliavaruudet
Line U as a subspace
Ch 11. Linear independence
3D: plane
in space (ggb)
Ch 12. Basis, coordinates and dimension
Ch 17. Change of basis
Linear
Space and Basis (wider worksheet)
Ch 13. Subspaces associated to a matrix
Ch 14. Linear functions (JSXgraph)
Basic linear
functions in the plane
Ch 15. Linear functions and subspaces
Lineaarikuvauksen
toiminta
Ch 16. Matrix representation of linear functions
Linearity
of functions and matrix representation (wider worksheet 1)
Ch 18. Inner product space
Ch 19. Orthogonal sets - projections
Projections
1 to be revised
Projection to a subspace (R3 to
a plane)
Ch 20. Orthonormal basis and matrices
Ch 21. Orthonormal subspaces and LSQ-method
Visualisation of 3x2-matrix LSQ
PNS, yhtälöryhmät ja suorat
tasossa
Tason suorat ja PNS - tulkintaongelma
(teoriaa ja tehtäviä, PNS-ratkaisun geometrinen konstruointi)
Projection
matrix P to be revised
Visualization of Problem 21.5.2
(Maple worksheet)
Visualization of Problem 21.6.2 (Maple
worksheet)
Visualization of Problem 21.6.3 (Maple
worksheet)
Ch 22. Curve fitting by LSQ
Fitting of a straight line
Ch 23. Eigenvalues and eigenvectors
Eigenvalues and eigenvectors
of 2x2-matrix (and the assciated linear function)
Object
images under linear functions, determinant, eigenvectors (wider worksheet
2)
Ch 24. Diagonalization of matrices
To be done
Ch 25. Symmetric matrices and the Spectral Theorem
To be done
Ch 26. About quadratic forms
To be done