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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
Matrices and their algebra, Gauss-Jordan elimination
Vector spaces, bases and dimension
Subspaces, nullity and rank, sums, direct sums, direct products
Linear maps, isomorphisms
Matrices associated to linear maps,
Change of basis
Linear transformations in geometry
Midterm I
Determinants, characteristic polynomial, Eigenvalues, Eigenvectors, eigenspaces
Similar matrices, diagonalizing matrices
Inner products
Orthogonal bases, Gram-Schmidt orthogonalization
QR-factorization
Orthogonal transformations and orthogonal matrices
Sylvestre's theorem and dual space
Curve fitting
Quadratic forms
Symmetric matrices and spectral theorem
Midterm II
Graphing quadratic surfaces, principal axes theorem
Positive definite matrices
Singular Value Decomposition
Further topics
Review
Final Exam
Other Literature:
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