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Great Intro to the Subject
Lots of Writing
Not too easy. Not too difficult.
This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines. Linear algebra is a branch of mathematics that studies systems of linear equations and the properties of matrices. The concepts of linear algebra are extremely useful in physics, economics and social sciences, natural sciences, and engineering. Due to its broad range of applications, linear algebra is one of the most widely taught subjects in college-level mathematics (and increasingly in high school).
After successfully completing the course, you will have a good understanding of the following topics and their applications: Systems of linear equations Row reduction and echelon forms Matrix operations, including inverses Block matrices Linear dependence and independence Subspaces and bases and dimensions Orthogonal bases and orthogonal projections Gram-Schmidt process Linear models and least-squares problems Determinants and their properties Cramer's Rule Eigenvalues and eigenvectors Diagonalization of a matrix Symmetric matrices Positive definite matrices Similar matrices Linear transformations Singular Value Decomposition
Hours per week:
Advice for students:
To succeed in this course you will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems. This material is presented in the first few lectures of 18.02 Multivariable Calculus, and again here. The basic operations of linear algebra are those you learned in grade school – addition and multiplication to produce "linear combinations." But with vectors, we move into four-dimensional space and n-dimensional space!