### Lecture Outlines (Linear Algebra for Engineers)

 Bahman Gharesifard Winter 2015

Course webpage: APSC 174

### Lectures:

 Lecture 1: (The language of sets) Lecture 2: (Maps between sets) Lecture 3: (Systems of linear equations) Lecture 4: (Vector spaces) Lecture 5: (Example of vector spaces) Lecture 6: ("Proofs" using axioms: properties of vector spaces) Lecture 7: (Vector subspaces I) Lecture 8: (Vector subspaces II) Lecture 9: (Linear combinations) Lecture 10: (From linear combinations to linear equations) Lecture 11: (Linear independence and dependence I) Lecture 12: (Linear independence and dependence II) Lecture 13: (From belonging to a span to existence of solutions to linear equations I) Lecture 14: (From belonging to a span to existence of solutions to linear equations II) Lecture 15: (From belonging to a span to existence of solutions to linear equations III) Lecture 16: (Matrices and row operations I) Lecture 17: (Matrices and row operations II) Lecture 18: (Solving systems of linear equations) Lecture 19: (Generating sets) Lecture 20: (Bases and coordinates) Lecture 21: (Dimension of a vector space) Lecture 22: (Linear transformations) Lecture 23: (Image of a linear transformation) Lecture 24: (Kernel of linear transformation) Lecture 25: (From linear transformations to matrices, and back) Lecture 26: (Image and kernel of matrices) Lecture 27: (The rank-nullity theorem) Lecture 28: (From linear transformations to linear equations, and back) Lecture 29: (Operations on matrices I) Lecture 30: (Operations on matrices II) Lecture 31: (Invertible linear transformations) Lecture 32: (Determinants) Lecture 33: (Eigenvalues and Eigenvectors I) Lecture 34: (Eigenvalues and Eigenvectors II) Lecture 35: (Eigenvalues and Eigenvectors III)

For questions, contact me with bahman at mast.queensu.ca or with 613-533-2441 (I prefer emails)