Matrices and linear transformations, determinants, eigenvalues, eigenvectors, diagonalization, factorization.
The purpose of MAT 22A is to introduce students to the fundamental objects and concepts in Linear Algebra, including scalars, vectors, matrices, diagonal matrices, symmetric matrices, inverse matrices, singular & nonsingular matrices, permutation matrices, linear combination, linear dependence & independence, vector spaces, subspaces, the dimension of a vector space, bases of vector spaces, rank, nullity, the four fundamental subspaces associated with a matrix, projections, determinants, permutations and cofactors, and eigenvectors & eigenvalues, and the fundamental operations on these objects including the dot product, matrix multiplication, matrix transpose, Gaussian elimination, GaussJordon elimination, LU decomposition, matrix factorizations, reduction of a matrix to row reduced echelon form (RREF), the solution of systems of linear equations in an arbitrary number of unknowns, the least squares procedure and the GramSchmidt procedure. In MAT 22A a modern, innovative approach is taken in presenting this material. This approach gives students an introduction to logic and proof, which is one of the goals of this course.
Download syllabus here.
Textbook link here.
August 5  August 6  August 7  August 8  August 9 

What is Linear Algebra  Gaussian Elimination & Row Operations  Homework 1 Due  Solution Sets & Vectors  
Chapter 1 Notes 
Sections 2.1, 2.3 Notes 
Homework Solutions 
Sections 2.5, Chapter 4 Notes 

August 12  August 13  August 14  August 15  August 16 
Vector Spaces & Linear Transformations  Homework 2 Due  Midterm 1  Matrices & Their Properties  
Chapters 5, 6 Notes 
Homework Solutions 
Chapters 12, 46 Study Guide Solutions Extra Credit EC Solutions 
Sections 7.1, 7.3 Notes 

August 19  August 20  August 21  August 22  August 23 
Inverse Matrices & LU Decomposition  Determinants  Homework 3 Due  Subspaces and Linear Independence  
Sections 7.5, 7.7 Notes 
Chapter 8 Notes 
Homework Solutions 
Chapters 9, 10 Notes 

August 26  August 27  August 28  August 29  August 30 
Basis, Dimension, Kernel, Range, Nullity, & Rank  Homework 4 Due  Midterm 2  Eigenvalues & Eigenvectors, Diagonalization  
Chapters 11, 16 Notes 
Homework Solutions 
Chapters 711, 16 Study Guide Additional Problems Solutions Extra Credit 
Chapters 12, 13 Notes 

September 2  September 3  September 4  September 5  September 6 
Labor Day  Orthonormal Bases and Complements  Homework 5 Due  Symmetric Matrices and Least Squares  
Chapter 14 Notes 
Homework Solutions 
Chapters 15, 17 Notes 

September 9  September 10  September 11  September 12  September 13 
Singular Value Decomposition  Homework 6 Due  Review Day The Simplex Method 
Final Exam  
Chapter 17 PCA Example Notes 
Homework Solutions 
Chapters 117 Notes 
Chapters 12, 417 Study Guide Additional Problems Solutions 