This course will cover classical linear algebra and its modern applications, such as in Google's TensorFlow or PyTorch and various data representation packages. Topics include vectors, matrices, systems of linear equations, dot and cross products, determinants, linear independence, bases, abstract vector spaces, Fourier bases; linear transformations, change of basis, and similarity. Eigenvalues, eigenvectors, and diagonalization. Inner product space, orthonormal basis, Gram Schmit methods, and orthogonal diagonalizing symmetric matrix. Additional topics, including Principal Component Analysis, Singular Value Decomposition and dimension reduction in Big Data analysis.