# Math 225 Linear Algebra and Matrix Theory

The official syllabus in pdf form.

The text Linear Algebra, 4th Edition by Friedberg, Insel, and Spence will be referred to as FIS.

Weekly problem sets will be due in class on Thursday.

## Weekly Syllabus and Homework

Updated April 24, 2015.

 Week Date Topics Reading Homework 1 Tue 13 Jan History of linear algebra. Classical notion of vector. Vector spaces. Examples of vector spaces. FIS 1.1, 1.2 Thu 15 Jan More examples and basic properties of vector spaces. Review of complex numbers and fields. FIS 1.2, Appendix C, D 2 Tue 20 Jan Subspaces. FIS 1.3 Problem Set #1 Thu 22 Jan Linear combinations. Span. Systems of linear equations. FIS 1.4 3 Tue 27 Jan Nor'easter Juno! Thu 29 Jan Linear dependence/independence. Basis. FIS 1.5, 1.6 4 Tue 03 Feb Basis. Dimension. Linear transformations. FIS 1.6, 2.1 Problem Set #2 Thu 05 Feb Quiz 1. Linear transformations. Null space. Range. Rank-Nullity Theorem. One-to-one and onto. FIS 2.1 5 Tue 10 Feb Review of bases. Coordinate vector. Matrix representation of a linear map. FIS 2.2 Problem Set #3 Thu 12 Feb Space of linear maps. Composition of linear transformations. Matrix multiplication. FIS 2.2, 2.3 6 Tue 17 Feb Left multiplication transformations. Inverse of a linear transformation. FIS 2.3, 2.4 Problem Set #4 Thu 19 Feb Isomorphism. Change of coordinates. FIS 2.4, 2.5, 7 Tue 24 Feb Change of coordinates. Elementary row and column operations. Elementary matrices. Rank of a matrix. Matrix inverse. FIS 2.5, 3.1, 3.2 Problem Set #5 Thu 26 Feb Gaussian elimination using row and column operations. FIS 3.2 8 Tue 03 Mar Reduced row echelon form. Homogeneous/inhomogeneous systems. FIS 3.3, 3.4 Midterm review Review Solutions Thu 05 Mar Midterm exam! 9 Tue 10 Mar Spring Break! Thu 12 Mar Spring Break! 10 Tue 17 Mar Spring Break! Thu 19 Mar Spring Break! 11 Tue 24 Mar Determinants. FIS 4.1, 4.2, 4.3 Problem Set #6 Thu 26 Mar More determinants. Eigenvalues and eigenvectors. Diagonalization. FIS 4.3, 5.1, 5.2 12 Tue 31 Mar Characteristic polynomial. Eigenspaces. Diagonalization. FIS 5.1, 5.2 Problem Set #7 Thu 02 Apr Google PageRank algorithm 13 Tue 07 Apr Google PageRank (revisited). Multiplicity of eigenvalues. FIS 5.2 Problem Set #8 Thu 09 Apr Inner product spaces. Norms. Orthogonal vectors. Orthonormal basis. Quiz 2. FIS 6.1, 6.2 14 Tue 14 Apr Gram-Schmidt orthogonalization process. FIS 6.2 Problem Set #9 Thu 15 Apr Adjoint of a linear transformation. Normal and self-adjoint operators. Spectral Theorem for normal operators. FIS 6.3, 6.4 15 Tue 21 Apr Spectral Theorem for self-adjoint operators. Quadratic forms. FIS 6.4 Problem Set #10 Thu 23 Apr Heisenberg's uncertainty principle. 16 Tue 28 Apr Reading period. Final Exam Review Solutions Tue 05 May Final Exam!