Vector algebra and geometry of three-dimensional Euclidean space and extensions to n-space and vector spaces; lines and planes, matrices, linear transformations, systems of linear equations, dimension, rank, determinants, eigenvalues and eigenvectors, and diagonalization. Additional topics may include singular value decomposition.
This course introduces students to vectors, linear transformations, and matrices with applications to geometry, data science, and more. The course usually begins with a careful study of the solution of linear systems of equations and ends with the orthogonal diagonalization of symmetric matrices. Topics include basic concepts and computation of determinants, bases, dimension, rank, nullity, eigenvalues, and eigenvectors. Only students who did very well in Calculus I should attempt this course before completing a full year of calculus.