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Lecture Notes

Note: Reduced means 4 viewgraphs per page. Full size is one per page.
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• Set number 16 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Apr 23 06:59:21 CDT 2018
  Topics: Eigenvalues end eigenvectors; Diagonalization; The Singular value decomposition; Applications.

• Set number 15 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Apr 16 07:55:03 CDT 2018
  Reposted Thu Apr 26 14:37:45 CDT 2018 Pages 15-14 to 15-15 added.
  Topics: Orthogonality and least-squares - continued; Orthogonal systems of vectors; The Gram-Schmidt algorithm; The QR factoriozation. Least-squares via QR

• Set number 14 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Apr 5 18:18:27 CDT 2018. Reposted Fri Apr 6 07:16:52 CDT 2018.
  Topics: Orthogonality and least-squares problems; Inner products and norms; Basic inequalities; Orthogonal spaces; Least-squares problems; Applications.

• Set number 13 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Apr 3 15:11:55 CDT 2018
  Topics: Application: mappings. Representing rotations, translations Combining rotations and translations, Homogenous coordinates

• Set number 12 : Full size: PDF.   Reduced: PDF .   Posted on: Fri Mar 30 09:31:24 CDT 2018
  Topics: Linear independence revisited; Bases; Standard bases; Bases for the null space and for the column space; Dimension of a subspace; Rank of a matrix.

• Set number 11 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Mar 22 15:10:09 CDT 2018
  Topics: General vector spaces; Examples; Subspaces; The Null and the Column space of a matrix.

• Set number 10 : Full size: PDF.   Reduced: PDF .   Posted on: Thu Mar 8 09:04:44 CST 2018
  Topics: Determinants. Properties of 2x2 determinants; General definition of nxn determinants; cofactors; Applications: matrix inversion, areas in 2-dimens. spaces; Volumes in 3-dimens. spaces.

• Set number 9 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Feb 26 18:17:49 CST 2018
  Topics: The LU factorization; Motivation; Elimination matrices; How to compute L; Applications of the LU factorization.

• Set number 8 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Feb 18 16:17:08 CST 2018   Re-posted Fri Mar 2 11:29:03 CST 2018 with changes and additions at end
  Topics: The inverse of a matrix; Point of view of mappings; Properties; General results on existence of the inverse; Elementary matrices and the inverse; Computing the inverse

• Set number 7 : Full size: PDF.   Reduced: PDF .   Posted on: Mon Feb 12 17:42:51 CST 2018;   Re-posted Wed Feb 21 08:06:56 CST 2018 with additions (3 pages after p. 7-8)
  Topics: Linear Mappings; Linear vs. nonlinear mappings; Matrices as mappings; Matrices; Matrix operations; Transposition; Addition or matrices; Product of matrices.

• Set number 6 : Full size: PDF.   Reduced: PDF .   Tue Feb 6 17:47:23 CST 2018 and Re-posted on: Fri Feb 9 17:58:14 CST 2018 with additions at end.
  Topics: The matrix equation Ax=b. Matrix-vector products; Existence of solutions. Application: Markov chain models. Application: Economic models; Google PageRank.

• Set number 5 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Jan 31 09:03:55 CST 2018
  Topics: Vectors and the space R^n; operations with vectors; Linear combinations of vectors; The span of a set of vectors; Geometric representations; Linear Independence of vectors; Determining linear independence.

• Set number 4 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Jan 24 08:43:25 CST 2018
  Topics: Matlab: explanation of gauss.m script; The row echelon form; reduced row echelon form; Computing the standard and reduced row echelon form; Applications; General solution of a linear system.

• Set number 3 : Full size: PDF.   Reduced: PDF .   Posted on: Sun Jan 21 09:48:43 CST 2018
  Topics: Sec. [1.1] from text; Solving Systems of equations; Augmented form; Equivalent systems; Row operations; Gaussian elimination; Pivoting; Gauss-Jordan Elimination.

• Set number 2 : Full size: PDF.   Reduced: PDF .   Posted on: Wed Jan 17 18:17:52 CST 2018
  Topics: A brief introduction to Matlab; Getting help; Simple matlab commands; If statements; Loops; Array constructs; Simple plotting.

• Set number 1 : Full size: PDF.   Reduced: PDF .   Posted on: Tue Jan 16 13:00:38 CST 2018
  Topics: Background algorithms; Complexity; Linear Systems; Solving triangular systems.