This course introduces students to linear algebra principles that form the foundation of data science. Students will use Python to write simple programs to implement linear algebra concepts. Linear algebra concepts will be connected to important biomedical data science problems, such as text representation.
- Vector and matrix representation and basic mathematical operations
- Vector spaces
- Gaussian elimination
- Basis vectors, dimensionality, norm
- Null space, column space, and row space
- Orthogonal projections
- Least squares
As part of this class, students will develop a simple Python package that implements vectors, matrices, and linear algebra functions. Because the objective of the programming is to reinforce linear algebra principles, programs will be developed from native Python data structures rather than numpy, which would be used in practice.
Students should have prior Python programming experience (such as the DeCART Python boot camp or equivalent).
- Linear Equations
- Systems of linear equations
- Row reduction - Gaussian elimination
- Vector equations
- Matrix equations
- Solutions sets
- Linear independence
- Matrices
- Linear transformations
- Matrix operations
- Inverses of matrices
- Vector Spaces
- Vector spaces
- Null space
- Column space, row space
- Linearly independent sets, bases
- Coordinate systems, dimension
- Orthogonality and Least Squares
- Inner products
- Orthogonal sets
- Orthogonal projections
- Least-Squares