Review of Linear Algebra

MSAN 502 - Review of Linear Algebra

Instructor: Some Mathematician

Course Syllabus

Summer 2013

SUMMARY INFORMATION

Instructor: Some Mathematician

Office: [UNKNOWN]

Office Hours: [UNKNOWN]

Cell Phone: [UNKNOWN]

Email Address: [UNKNOWN]

Class Location: 101 Howard Street, Room 451

Class Time: 10:00 a.m. - 12:00 noon on Mondays and Tuesdays


ON COURSE OBJECTIVES. Any student who successfully completes this boot camp should:

  • Understand the definitions of real-valued vectors and matrices;
  • Recall elementary operations on vectors and matrices, e.g., scalar multiplication, addition, multiplication;
  • Recall other standard definitions from linear algebra, e.g., transpose of a matrix, symmetric matrix, diagonal of a matrix, identity matrix, trace of a matrix, upper triangular matrices, nilpotent matrices, exponential of a matrix, etc.;
  • Recall basic definitions, facts, and techniques connected with the solution of systems of linear equations, e.g., Gauss-Jordan elimination, the inverse of a matrix, Cramer's rule, etc.;
  • Understand the definition of, properties of, and numerical evaluation of the determinant of a matrix;
  • Recall the definitions of, and examples of, vectors spaces, inner products, orthogonality, projection, and the Gram-Schmidt procedure;
  • Define, and work with examples of, subspaces of vector spaces, linear dependence and independence, basis and dimension, change of basis, the rank of a matrix, and orthonormal vectors in Rn;
  • Define, and understand the significance of, orthogonal and orthonormal matrices;
  • Define, and understand the significance of, eigenvalues and eigenvectors;
  • Perform diagonalization of matrices by hand and in R, i.e., effect the eigendecomposition (or spectral decomposition) of square matrices;
  • Understand that not every square matrix is diagonalizable;
  • Define, and understand the signicance of, positive definite matrices and quadratic forms;
  • Define, and compute, the condition number of the linear equation A:x = b; and
  • Understand, and be able to implement in R, the classical matrix decompositions (LU decomposition, singular value decomposition, and Cholesky decomposition).