Math 260 - Linear Algebra
UMass Boston
Summer 2013

Lectures

• July 15, 2013: Introduction. The space R^n. Linear combinations. Linear decompositions.
• July 16, 2013: Planes in space. Linear systems. Matrices and augmented matrices.
• July 17, 2013: Product of matrix and vector. Row operations. Elimination algorithms: Gauss-Jordan and Gaussian elimination.
• July 18, 2013: RREF and REF. Solutions of linear systems.
• July 22, 2013: Matrix algebra. Elementary matrices. Inverse matrix. Column operations.
• July 23, 2014: Fundamental forms. Data compression. Column Space. Linear subspaces.
• July 24, 2013: Redundancies. Linear dependencies. Bases of column spaces. Bases of linear subspaces.
• July 25, 2013: Null Space. Bases. Coordinates. Dimension.
• July 29, 2013: First Exam
• July 30, 2013:
• July 31, 2013:
• August 1, 2013:
• August 5, 2013: Matrix of a transformation in given bases.
• August 6, 2013: Fundamental form of a linear transformation.
• August 7, 2013: Dot product and norm. Orthonormal bases.
• August 8, 2013: Orthonormalization and QR-decomposition
• August 12, 2013: Second Exam. Orthogonal complement
• August 13, 2013: Orthogonal projections. Least squares.
• August 14, 2013: Determinants. Expansions. Row operations.
• August 15, 2013: Determinant of a transformation. Discrete dynamical systems. Diagonalization.
• August 19, 2013: Eigenpackage: eigenvalues, eigenvectors, eigenspaces, eigenbases. Examples.
• August 20, 2013: Geometric and algebraic multiplicities. Rigid diagonalization. Conics.
• August 21, 2013: Conics - reduction to canonical form. Further topics: SVD, spaces of functions.
• August 22, 2013: Third Exam