Linear algebra problems, their importance, and computational difficulties -- A review of some required concepts from core linear algebra -- Floating point numbers and errors in computation -- Stabilityof algorithms and conditioning of problems -- Gaussian elimination and LU factorization -- Numerical solutions of linear systems -- QR factorization, singular value decomposition, and projections -- Least-squares solutions to linear systems -- Numerical matrix eigenvalue problems -- Numerical symmetric eigenvalue problem and singular value decomposition -- Generalized and quadratic eigenvalue problems -- Iterative methods for large and sparse problems : an overview -- Some key terms in numerical linear algebra.