Together with calculus, linear algebra is one of the foundations of higher level mathematics and its applications. There are several perspectives one can take on linear algebra: it is a method for handling large systems of equations, it is a theory of higher dimensional geometry, and it is a theoretical construct that appears throughout mathematics and physics, among other things. This course will cover both the applied and theoretical aspects, with enough optional material to allow students to focus primarily on one or the other. Applications include correlation coefficients and linear regression in statistics, finite element methods in physics and engineering, interaction networks and clade analysis in biology, and google page rank and data compression in computing. The course will also set students up for more advanced applications in quantum mechanics, fourier analysis, and number theory. This course is a prerequisite for Multivariable Calculus. Topics include axiomatic vector spaces, the spectral theorem, decomposition theorems, and multilinear algebra.