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 realvalued 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., GaussJordan 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 GramSchmidt 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).

