**Lecture Schedule**

8/22 Introduction, key facts about matrix multiplication, 4 ways to view matrix multiplication, upper/lower trangular (UT/LT) matrices, solving Ax=b for an UT matrix, review of Gauss Elimination

8/24 Gauss Elimination, LU decomposition, permutation matrice, pivots

8/29 PA=LDU decomposition, computational cost of LU decomposition, inverses

8/31 Gauss-Jordan algorithm to compute matrix inverse, transpose and properties, symmetric matrices

9/5 Linear regression (example of Ax=b), vector spaces and their subspaces

9/7 Matlab for linear systems demo, null space and column space of a matrix, Echelon form of a matrix

9/12 Campus closed

9/14 Reduced form of a matrix and using it to compute the null and column spaces

9/19 Independence of vectors, bases, dimension

9/21 Exam 1

9/26 The four fundamental subspaces and the Fundamental Theorem of Linear Algebra I, Rank theorem

9/28 Existence and uniqueness of solutions of Ax=b, left and right inverses, rank-1 matrices, linear transformations

10/3 Linear transformations including differentiation and integration on polynomials, matrix representation of a linear transformation

10/5 Inner products and orthogonality, Fundamental theorem of orthogonality, Fundamental Theorem of Linear Algebra II, Fredholm's alternative, projection

10/12 Orthogonal projection, best approximate solution to Ax=b

8/24 Gauss Elimination, LU decomposition, permutation matrice, pivots

8/29 PA=LDU decomposition, computational cost of LU decomposition, inverses

8/31 Gauss-Jordan algorithm to compute matrix inverse, transpose and properties, symmetric matrices

9/5 Linear regression (example of Ax=b), vector spaces and their subspaces

9/7 Matlab for linear systems demo, null space and column space of a matrix, Echelon form of a matrix

9/12 Campus closed

9/14 Reduced form of a matrix and using it to compute the null and column spaces

9/19 Independence of vectors, bases, dimension

9/21 Exam 1

9/26 The four fundamental subspaces and the Fundamental Theorem of Linear Algebra I, Rank theorem

9/28 Existence and uniqueness of solutions of Ax=b, left and right inverses, rank-1 matrices, linear transformations

10/3 Linear transformations including differentiation and integration on polynomials, matrix representation of a linear transformation

10/5 Inner products and orthogonality, Fundamental theorem of orthogonality, Fundamental Theorem of Linear Algebra II, Fredholm's alternative, projection

10/12 Orthogonal projection, best approximate solution to Ax=b