# Prep 2011 workshop Linear Algebra

(Difference between revisions)

# Working page for the Linear Algebra group at PREP 2011

## Preliminary Topic List - 2011-06-23

• Vectors
• Geometric objects - lines and planes
• Dot product
• Projection
• Orthogonal decomposition
• Systems of equations and elimination
• Row operations and Row Echelon Form
• Gaussian elimination (Free variables & Consistency of solutions)
• Matrix operations and algebra
• Matrix arithmetic
• Matrix inverse
• Matrix equations
• Determinant
• Elementary matrices
• LU
• Vector space preliminaries
• Definition of a vector space and subspaces
• 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 and rank
• Geometric examples
• Linear transformations
• Matrix of a linear transformation
• Reflections, rotations, dilations and projections
• Inverse of a transformation
• Kernel, range, injection, surjection
• Applications
• Least squares
• Curve/surface fitting
• Mixture problems
• Simplex method
• Graph theory
• Approximation of a function by a Fourier polynomial
• Eigenvalues and eigenvectors
• Finding eigenvalues and eigenvectors
• Eigenspaces
• Diagonalization
• Symmetric matrices & Trace
• Note: There are some "trace" problems in the NPL in Linear Algebra/Matrices/Matrix Operations