Prep 2011 workshop Linear Algebra: Difference between revisions

Revision as of 18:16, 23 June 2011

Preliminary Topic List

Vectors
- Geometric objects - lines and planes
- Dot product
- Projection
- Orthogonal decomposition
Systems of equations and elimination
- Free variables
- Consistency of solutions
- Gaussian elimination
Matrix operations and algebra
- Matrix arithmetic
- Matrix inverse
- Matrix equations
- Determinant
- Elementary Matrices
- LU
Vector Space Preliminaries
- Definition of a vector space
- Euclidean vector spaces
- linear combinations and span
- linear independence
- basis and orthogonal basis
- coordinate vectors and change of basis
- row space, column space, and null space
- dimension
- geometric examples
Linear transformations
- Matrix of a linear transformation
- Reflections, rotations, dilations and projections
- Inverse of a transformation
Applications
- Adjacency matrix
- Least squares
- Curve/surface fitting
- Mixture problems
- Simplex method
- Graph theory
Eigenvalues and eigenvectors
Inner product spaces and abstract vector spaces

@@ Line 12: / Line 12: @@
 ** Matrix arithmetic
 ** Matrix inverse
+** Matrix equations
 ** Determinant
 ** Elementary Matrices
@@ Line 18: / Line 19: @@
 ** Definition of a vector space
 ** Euclidean vector spaces
-** Span
+** linear combinations and span
 ** linear independence
 ** basis and orthogonal basis
-** row space
+** coordinate vectors and change of basis
-** column space
+** row space, column space, and null space
-** null space
 ** dimension
 ** geometric examples
 * Linear transformations
 ** Matrix of a linear transformation
-** Geometric transformations
+** Reflections, rotations, dilations and projections
+** Inverse of a transformation
 * Applications
 ** Adjacency matrix