Linear Algebra

Course Outline

Vectors and vector algebra in the plane and space. Geometric meaning of solving linear systems. Matrix algebra. Vector spaces and subspaces. Linear independence. Linear systems and matrices.  Solving linear systems, Gaussian elimination and LU factorization. Basis and dimension of a vector space. The four subspaces defined by a matrix. Rank of a matrix. Rank factorization. Inner product spaces Orthogonality, Projection matrix. Gram-Schmidt orthonormalization. The linear least squares problem. Matrix trace and determinant. The characteristic polynomial of a matrix, eigenvalues, eigenvectors, and eigenspaces. Jordan canonical form. Singular value decomposition. The matrix pseudo-inverse. Linear transformations and its associated matrix