Credits -- 3 (3-0-0)
Term Offered -- Fall
Topics --
- Vector Spaces
scalar field
span
subspace
linear dependence and independence
basis and dimension
extension to a basis
direct sum decompositions
- Linear Transformations
matrix operators
range
nullspace
rank
singularity and nonsingularity
linear functionals
representations
- Linear Equations
fields
systems of linear equations
matrices and elementary row operations
row-reduced echelon matrices
matric multiplication
invertible matrices
- Inner Products and Norms
inner products
orthogonality
norms
adjoints (and transposes)
symmetry and self-adjointness
positive definiteness
positive definite symmetric
Gram-Schmidt process
matrix norms
- Invariant Subspaces
eigenvalues and eigenvectors
geometric and algebraic multiplicities
characteristic polynomials
eigenstructure of symmetric matrices
eigenfunction expansions
generalized eigenvectors
Jordan form
singular value decompsoition