Linear Algebra and Component Analysis

3 units

Linear algebra is the foundation of scientific computing across many disciplines of engineering. This course will introduce the numerical and computational issues that arise from solving large-scale problems, with motivation from data science, machine learning, and signal processing. Topics to be covered include least-squares problems, eigenvalue/eigenvector analysis, singular value decomposition, component analysis, rotation of bases, and concepts of computational complexity and numerical stability. A focus of the class will be studying concepts from signal processing and machine learning such as K-means, Fourier analysis, wavelet analysis, and sampling within the framework of linear algebra. The course will include case studies touching on a broad range of topics including systems science, signals and imaging, devices and circuits, and quantum science/applied physics.