Linear Algebra and Component Analysis

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.