Catalog Description
Study of general vector spaces, linear systems of equations, linear transformations and compositions, Eigenvalues, eigenvectors, diagonalization, modeling and orthogonality.
Contents
A word on Analytic Geometry, Vectors in Physics and Geometry
Euclidean spaces, norm and dot product  Â
Matrices and their algebra, Gauss-Jordan elimination Â
Vector spaces, bases and dimension Â
Subspaces, nullity and rank, sums, direct sums, direct productsÂ
Linear maps, isomorphisms
Matrices associated to linear maps, Â
Change of basisÂ
Linear transformations in geometryÂ
Midterm I
Determinants, characteristic polynomial, Eigenvalues, Eigenvectors, eigenspaces Â
Similar matrices, diagonalizing matrices
Inner productsÂ
Orthogonal bases, Gram-Schmidt orthogonalizationÂ
QR-factorization
Orthogonal transformations and orthogonal matrices
Sylvestre's theorem and dual space
Curve fittingÂ
Quadratic forms
Symmetric matrices and spectral theorem
Midterm II
Graphing quadratic surfaces, principal axes theoremÂ
Positive definite matrices
Singular Value Decomposition
Further topics
Review
Final Exam